What is 2nd order: Definition and 494 Discussions

The Order of the Patriotic War (Russian: Орден Отечественной войны) is a Soviet military decoration that was awarded to all soldiers in the Soviet armed forces, security troops, and to partisans for heroic deeds during the German-Soviet War, known since the mid-1960s in the former Soviet Union as the Great Patriotic War.

View More On Wikipedia.org
Recent contents Top users
  1. karush

    MHB -17.2.02 - Solve 2nd order ODE using undetermined coefficients.

    $\tiny{17.2.02}$ \nmh{1000} $\textrm{Solve the equation by the method of undetermined coefficients.}\\$ \begin{align*}\displaystyle y''-4y'&=\sin{x}\\ y_p&=A\sin{x}\\ \end{align*} $\textit{ answer}$ \begin{align*}\displaystyle y{\left (x \right )}& = C_{1} + C_{2} e^{4 x} - \frac{1}{17}...
  2. B

    A Test if 2nd order diff eq. can be derived from a Hamiltonian

    Imagine I have a complicated second-order differential equation that I strongly suspect can be derived from a Hamiltonian (with additional momentum dependence beyond p2/2m, so the momentum is not simply mv, but I don't know what it is). Are there any ways to test whether or not the given...
  3. M

    I Analyzing a 2nd Order Non-Linear ODE with Variable Substitution

    Can someone check my work here? Both ##f=f(x)## and ##y=y(x)##. $$f'y'+\frac{fy''}{1+y'^2}=0\implies\\ \frac{y''}{y'(1+y'^2)}=-\frac{f'}{f}\\ \frac{y''}{y'(1+y'^2)}=-\ln(f)$$ Now let ##v=y'##, which implies $$...
  4. R

    I 2nd order differential equation problem with sin(theta)

    I have a differential equation that is essentially this: θ''(t)=c*sin[θ(t)] . I've been stymied trying to find a solution, and even when I tried using Maple, I got a nasty integral of a Jacobian amplitude. I'm tempted to use a small angle approximation, but the angle is 0≤θ≤π/2. I know this...
  5. Kanashii

    4th order RK to solve 2nd order ODE

    Homework Statement Consider the initial value problem x" + x′ t+ 3x = t; x(0) = 1, x′(0) = 2 Convert this problem to a system of two first order equations and determine approximate values of the solution at t=0.5 and t=1.0 using the 4th Order Runge-Kutta Method with h=0.1. Homework Equations...
  6. W

    2nd Order Linear ODE-Derivation of system-issue

    Homework Statement How exactly they combined equation1 and equation2 and got that system? I don't get that part. Homework Equations A*(dy/dt)= -k*y eq1 A*(dz/dt)=ky-kz eq2 The Attempt at a Solution I tried substituting the 1st ky in the 2nd equation and then differentiating but I don't...
  7. I

    Response of a 2nd order system

    Homework Statement Homework Equations N/A The Attempt at a Solution I understand how they got the answer and the calculations they did but I have 3 questions about this screenshot. 1) Why the box in red is the transfer function? Is there a way to tell this from the Y(s) = ... expression? 2)...
  8. MalachiK

    B How Do Jacobi Elliptic Functions Solve Nonlinear Differential Equations?

    I have ##\frac{d^2x(t)}{dt^2} + B(x(t))^3 = 0## for a system where I know the initial conditions and where B is a constant that's constructed from the properties of the system. I would like to find ##x(t)##. I've modeled the system in Python and produced some graphs. I know that ##x(t)## is...
  9. Valour549

    I 2nd Order Linear ODE w/ nonconstant coefficient

    xy'' + 2xy' - y = 0 Honestly no clue where to start, Wolfram Alpha gives a rather complex answer lol (http://www.wolframalpha.com/input/?i=xy%27%27%2B2xy%27-y%3D0)
  10. T

    Python Testing code to solve 2nd order wave equation

    As an exercise, I am trying to solve the 2nd-order wave equation: $$ \frac {\partial ^2 E}{\partial t^2} = c^2 \frac {\partial ^2 E}{\partial z^2} $$ Over a domain of (in SI units): ## z = [0,L=5]##m, ##t = [0,t_{max} = 5]##s, ##c = 1## m/s and boundary/initial conditions: ## E(z[0]=0,t) =...
  11. J

    Help finding general solution for 2nd order linear DE

    Homework Statement Find the general solution for the DE: t2y''-2y=0 Homework Equations These were given for other parts of the problem so I'm not sure if they're relevant. y1(t)=t2, y2(t)=t-1, y(1)=-2, y'(1)=-7 The Attempt at a Solution The t2 at the front was really stumping me and I'm not...
  12. F

    2nd order ODE boundary value constant input-- stuck

    Homework Statement Uxx - SU = A ; 0<x<1 Boundary conditions : Ux(0) = 0 U(1) = 0 The Attempt at a Solution I tried to set a new variable W = u + A, I can get rid of the A in the main equation and U(1) becomes = 1. If I set U= C*esqrt(S)x into the equation, its a trivial solution because of...
  13. R

    2nd order RC filter with two equal poles

    Is it possible to make a 2nd order CR LPF or HPF where the cut off frequencies for each pole are equal? Here is a calculator for this system which includes the transfer function.http://sim.okawa-denshi.jp/en/CRCRkeisan.htm I figured that I need to try to solve the denominator of the transfer...
  14. M

    MHB How Do I Solve this 2nd Order Non-Linear ODE and Find Its Equilibrium Points?

    Good morning everyone. First let me thank you for your help in advance! I have to solve this 2nd order non-linear ODE, and I'm stuck at the beginning. We have to find the equilibrium points, linearize the system, draw the phase portraits and classify the eq points, and solve it numerically. I...
  15. D

    2nd Order Control system PD controller

    Hi, This question on PD control is from a practice quiz. 1. Homework Statement If you can't see it- the question asks to find values for Kp and Kd such that the system achieves 5% OS and has a settling time Ts of 3s. Cs = 3 Cd = 2 m = 5Homework Equations ω_n^2/(s^2 + 2ζw_n + ω_n^2) - 2nd...
  16. F

    I General solution to linear homogeneous 2nd order ODEs

    Given a linear homogeneous 2nd order ODE of the form $$y''(x)+p(x)y'(x)+q(x)=0$$ the general solution is of the form $$y(x)=c_{1}y_{1}(x)+c_{2}y_{1}(x)$$ where ##c_{1},c_{2}## are arbitrary constants and ##y_{1}(x), y_{2}(x)## are linearly independent basis solutions. How does one prove that...
  17. W

    MHB Turning 2nd order into 1st order

    Good day all I am struggling with this one. m (d^2 h)/(dt^2 )+k dh/dt=-mg use v=dh/dt in place to turn 2nd order into 1st order so from this i have got (d^2 h)/(dt^2 )= -g-(v/m) Is this a first order equation? If so can somebody point me to solve the equation when m=80, k=8.7, v(0)=0ms-1...
  18. N

    I 4th order Runge-Kutta with system of coupled 2nd order ode motion equations

    MX''=Fn(cosΦ−usinΦ) MZ''=Fn(sinΦ+ucosΦ)−Mg MΦ''=Fn(Bxx+uBz) I tried using Runge-Kutta methods to approximate motion equations in MATLAB but it turn out wrong. I also tired finding and researching forums and web for solution but to no avail. Fn,M,θ,u is constant fn/M = 0.866 it seems that i...
  19. N

    4th order Runge Kutta Matlab with 2 2nd order ode

    Homework Statement Hi There! MX''=Fn(sin θ - uCos θ ) MZ''=Fn(cos θ + uSin θ ) - Mg Fn,M,θ,u is constant fn/M = 0.866 M = 6000 θ = 30 u = 0.5774 i split my motion equation into 2 individual 1st ode, X' = Vx Z' = Vz Vx'=[fn*(sin θ - uCos θ )]/M Vz'={[fn(cos θ + uSin θ )]/M} - g...
  20. I

    Help with my math in this 2nd order audio filter circuit

    I understand how to use the reactance equations (for capacitor, xc=1/(2PiFC), & for inductor xL=2PiFL when the filter circuit is of first order to get the component values I need, but I don't understand how the math works when the circuit is of second order. The man at the electronics store told...
  21. omar yahia

    A solved 2nd order ODE that i don't understand its solution

    { i feel that this is Not a smart question and that it is about the basics of something , but i tried to find the that "something" to know about it myself but i couldn't , as i couldn't name the issue , so i couldn't know what to search about that is why I'm asking here in a forum , so please...
  22. G

    Why 2nd order differential equation has two solutions

    Hello. I forgot the reason why 2nd order differential equation has two independent solutions. (Here, source term is zero) Why 3 or 4 independent solutions are not possible? Please give me clear answer.
  23. j3dwards

    2nd order differential equation (nonhomogenous)

    Homework Statement Find the general solution f(t) of the differential equation: f''(t) − f'(t) − 12f(t) = 36π . How many free parameters enter the solution, and why? Homework Equations f = fH + fP where fH is the homogeneous solution and fP is the particular solution. The Attempt at a...
  24. K

    2nd order ODE circuit, switch question

    if we assume the condition immediately after switch is closed (t=0+), *Capacitor voltage cannot jump. *Inductor current cannot jump. dv(0+)/dt=i_c(0+)/c di(0+)/dt=v_l(0+)/L which means we can find the initial condition of the post-zero system algebraically. However, it contradcits to the...
  25. dumbdumNotSmart

    Finding the homogenous solution of Var.Coeff. 2nd Order ODE

    It's been too long guys. I've given this ODE lots of thought and still no cigar. Homework Statement We are given the following ODE: $$ (x-a)y''-xy'+a^2y = a(x-1)^2e^x $$ and knowing that y=e^x is a solution to the homogenous equation, find the possible values of a. Next part: Using the...
  26. D

    Unclear concept on simple 2nd order differential eq

    Homework Statement Hi,I am learning to solve 2nd-order differential eq. Suppose I have a equation dy/dx - 3x = 0...(1) Then dy/dx = 3x -----> x = 3(x^2)/2 Now if I have a 2nd order ODE such that: d^2y/dx^2 = 3....(2) Then it could be solved by integrating both sides wrt x twice,which yields y...
  27. P

    Solve a 2nd order Ordinary Differential Equation

    Homework Statement Y''-((Y')^2)+(C1*exp(Y))=C2 C1 and C2 are constants. exp = e Homework Equations No clue how to start this The Attempt at a Solution Y'=A=dY/dt Y=At+C3 (not sure) A'-(A^2)+C1exp(At+C3)-C2=0 A'-(A^2)+C1exp(C3)exp(At)=0 let C=C1*exp(C3) A'-(A^2)+Cexp(At)=0
  28. T

    MHB Solving 2nd order differential equation numerically

    I'm writing a paper about the projectile motion with the consideration og air resistance - I have obtained two formulas: ax = k*(vx2+vy2)0.5 * vx ay = k*(vx2+vy2)0.5 * vy - g (K and g are constants; K = -0,02, g =9,82) I cand write these two as 2 different differential equations: v'x(t) =...
  29. D

    Demonstrate the matrix represents a 2nd order tensor

    Homework Statement Demonstrate that matrix ##T## represents a 2nd order tensor ##T = \pmatrix{ x_2^2 && -x_1x_2 \\ -x_1x_2 && x_1^2}## Homework Equations To show that something is a tensor, it must transform by ##T_{ij}' = L_{il}L_{jm}T_{lm}##. I cannot find a neat general form for ##T_{ij}##...
  30. K

    Transformation rule for product of 3rd, 2nd order tensors

    1. Problem statement: Assume that u is a vector and A is a 2nd-order tensor. Derive a transformation rule for a 3rd order tensor Zijk such that the relation ui = ZijkAjk remains valid after a coordinate rotation.Homework Equations : [/B] Transformation rule for 3rd order tensors: Z'ijk =...
  31. rayne1

    MHB General solution to 2nd order....

    I'm supposed to use undetermined coefficients to find a general solution to: y" + 4y' +3y =4^(-t) I can't find an example online where f(t) is equal to an exponential function that does not have e as the base, so I have no idea how to solve it. So far, I found the general solution to the...
  32. A

    Reduction of 2nd order PDE to a first order equations system

    I want to convert this linear second order general form PDE to two equations: ##ϕ_{xx}+bϕ_{xy}+cϕ_{yy}+dϕ_x+eϕ_y+fϕ=g(x,y)## Converted equations: ##a_1 u_x+b_1 u_y+c_1 v_x+d_1 v_y=f_1## ##a_2 u_x+b_2 u_y+c_2 v_x+d_2 v_y=f_2## I want to find parametric values of ##a_1 ...f_2## How can I do...
  33. FOIWATER

    2nd order approx. of barrier function

    Homework Statement write the 2nd order taylor series for the log barrier function $$-\sum_{i=1}^{m}(b_{i}-a_{i}^{T}x)$$ Homework Equations See Above The Attempt at a Solution Here is my attempt at a solution $$\nabla...
  34. B

    Solution for a general variational equation of 2nd order

    In a book of math, I found a kind very very crazy of equation, an "variational equation of second order" So, my question is: exist solution for an general equation like this: A \frac{d^2}{dx^2} \frac{\partial F}{\partial y^{(2)}} + B \frac{d^1}{dx^1} \frac{\partial F}{\partial y^{(1)}} + C...
  35. ognik

    MHB Use Wronskian to show only 2 indepndent solutions of 2nd order ODE

    Given standard ODE $ y'' + P(x)y' + Q(x)y=0 $, use wronskian to show it cannot have 3 independent sltns. Assume a 3rd solution and show W vanishes for all x. so 1st row of W = {$ {y}_{1}, {y}_{2},{y}_{3} $}, 2nd row is 1st derivatives, 3rd row is 2nd derivatives. I can find the determinate...
  36. kostoglotov

    Trial solution, undetermined coefficients, 2nd order non-homogeneous equation

    Homework Statement Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients. For: y'' + 2y' + 10y = x^2e^{-x}\cos{3x} There's a modification performed and I'm not 100% confident as to why. Homework EquationsThe Attempt at a Solution The...
  37. kostoglotov

    Question concerning 2nd order homogeneous linear diff eqs

    Homework Statement Regarding the case where the auxillary (characteristic) equation has complex roots, we solve the quadratic in the usual way using i to get the general solution y(x) = e^{\alpha x}\left(C_1 \cos{\beta x} + i C_2 \sin{\beta x}\right) And the textbook shows y(x) = e^{\alpha...
  38. Destroxia

    Series Solutions to a 2nd Order Diff. Eq.

    Homework Statement y'' + y' + xy = 0 Just want to make sure I understand this completely, I had a bit of trouble towards the end, and thought the -29/600 was a little weird of a fraction to be right. I wasn't given a correct answer to base mine off, so I'm not sure if I'm doing this all...
  39. Noctisdark

    How can the 2nd Order Elliptic Equation be solved for exact solutions?

    I've been searching for exact solution of d2y/dx2 = C/y, where C is some constant, such equation take place when deriving equation of motion in gravitationnal field, I'm more interested in how to solve it, yet I only managed to express it as power series using taylor's theorem at x = 0, just...
  40. Destroxia

    2nd Order Homogeneous, Real Roots, Initial Value

    Homework Statement Solve the initial value problem Homework Equations Quadratic Formula The Attempt at a Solution My problem is that I don't understand how to solve the constants now, I understand, 2 equations, 2 unknowns, but when I plug the y(0) = 0 into the YsubH equation...
  41. popopopd

    Existence of general solution, 2nd order ODE

    2nd order ODE has a form y''+p(x)y'+q(x)y=f(x)and if we assume f(x)=/=0 for every x, then y''+p(x)y'+q(x)y=/=0 so in this case we can't specify general solution of 2nd order ode?
  42. M

    Solving a 2nd Order Linear ODE: Any Clever Tricks?

    Homework Statement $$ay''-(2x+1)y'+2y=0$$ subject to ##y(0)=1## and ##y(1)=0## where ##a## is a non-zero constant. Homework Equations Not too sure The Attempt at a Solution I know an analytic solution exists since I solved with mathematica. My thoughts were to try a series expansion, but...
  43. H

    Convert 2nd order ODE to system of 1st order

    Homework Statement Convert the following second-order differential equation into a system of first-order equations and solve y(1) and y'(1) with 4th-order Runge-kutta for h=0.5. ##y''(t)+sin(y(t))=0,\ y(0)=1,\ y'(0)=0## Homework Equations The Runge-kutta method might be applicable, but I know...
  44. mudweez0009

    2nd Order, homogeneous Differential Equation

    Homework Statement Solve d2θ/dη2 + 2η(dθ/dη) = 0, to obtain θ as a function of η, where θ=(T-T0)/(Ts-T0) EDIT: I should add that this is a multi-part problem, and η is given as η=Cxtm. We had to use that to derive the equation in question above.. So I don't know if this is supposed to be...
  45. K

    2nd order pole while computing residue in a complex integral

    Hello, I am trying to understand how to get the residue as given by wolfram : http://www.wolframalpha.com/input/?i=residue+of+e^{Sqrt[x^2+%2B+1]}%2F%28x^2+%2B+1%29^2 The issue I am facing is - since it is a second order pole, when I try to different e^{\sqrt{x^+1}} I get a \sqrt{x^+1}...
  46. rakeru

    Finding Constants to Solution Given 2nd Order, Nonlinear DE

    Homework Statement Okay, here's the deal:I have been given a second order nonlinear differential equation, and I have also been given the general solution with constants A and B. I am supposed to find the constants A and B. The solution represents a fermion at rest, since the solution does not...
  47. engnrshyckh

    Finding the undamped natural frequency of 2nd order system

    the following 2nd order differential equation is given: 2y'' + 4y' +8y=8x........(1) i want to find damping ratio, undamped natural frequency, damping ratio coefficient and time constant for the above system. solution: comparimg (1) with general system equaion (veriable can be exchanged)...
  48. I

    MHB How to approach this 2nd order linear ODE?

    $y''+\frac{1}{x}y'=\frac{2}{x^2}-4$ Hey. This is probably really simple but I'm stuck :p how do I approach this?
  49. I

    MATLAB How can I solve a 2nd order ODE in matrix form using Matlab?

    I'm trying to solve a 2nd order differential equation in matrix form. I'm not familiar with Matlab, and have tried solving this using tutorials on youtube. Initially, theta1 = pi/4, theta2 = 7*pi/12, theta1_d = 0, and theta2_d =0. Time interval is (0,1.2). When I try to solve this using ode45...
  50. J

    2nd order resonance filter amplitude response(z-parameters)

    Homework Statement A resonance filter is a specific second-order digital system designed to attenuate all frequencies except at and around a given center frequency. The transfer function of a resonance filter is: H(z)=(1 - r)(1 - rz-2) / (1 - 2rcos(ωcT)z-1+r2z-2) where ωc = 2πfc, where fc is...
Back
Top