2nd order Definition and 464 Threads

I have put down the whole question and my answers which i would appreciate if someone could comment: Part 1.1 Find the general solution of the equation (d^2 z)/(dx^2 ) - 4 * dz/dx + 13z = 0 Put into form: a * m^2 + b * m + c ∴ m^2 - 4m + 13 = 0 a = 1, b = -4, c = 13 Then: m_(1,2 =...

Hello, i have a bit of a problem with uderestanding how exactly we use RK4 method for solving 2nd order ODE. And last conversation with my proffesor only added up to my confiusion. Further more i couldn't find any example dealing with this problem if any1 could provide link explaining this...

Homework Statement Could some mathematically minded person please check my calculation as I am a bit suspicious of it (I'm a physicist myself). This isn't homework so feel free to reveal anything you have in mind. Suppose I have two functions \phi(t) and \chi(t) and the potential V which...

Homework Statement y^{2}\frac{d^{2}y}{dx^2} + ay = b(cx-d) Find y as a function of x,a,b,c & d (a,b,c & d are all constant(!)) Homework Equations - The Attempt at a Solution Not a clue, this is actually how far I got with my own take on an orbital mechanics problem I made up...

y'' + 6y' + 4y = x(t) I found the eigenvalues to be -.764 and -5.24, no problems here. Next, since the order of the response is greater than the order of the excitation, I assumed the unit response took the form: h(t) = k_1e^{-.764t} + k_2e^{-5.24t} So now I must find the values for k_1 and...

Why is the characteristic of (d/dx) + (d/dt) = 0 where d is small delta c = x - t and not c = x + t

Homework Statement [PLAIN]http://img265.imageshack.us/img265/6778/complex.png I did the coefficient of the w' term. What about the w term? This seems like a fairly standard thing, but I can't seem to find it anywhere. What ansatz should I use for q, if the eqn is written w''+pw'+qw...

Homework Statement Find the solution of the following differential in the limit z -> i/2: Homework Equations Quotient rule, product rule. The Attempt at a Solution I found the first derivative using the quotient rule, with the answer as two fractions. I then took both fractions and...

Ok, so I've been studying the method of variation of parameters in order to solve 2nd order ODEs, and I have a question regarding a supposition that is made in the definition of the method. Say, y'' + p(t)y' + q(t)y = g(t) Then the general solution to the above equation is c_1y_1(t) +...

Homework Statement 1.a) Taking the Schrodinger second order differential equation given, split it into two first order differential equations for numerical solving. We're given the relevant constants in a table, such as \hbar, \alpha, etc. 'z' is taken to be an indepedent variable which we...

1. Using the complementary function and particular integral method find the solutio of the differential equation. d2y/dx^2 + 3 dy/dx +2y = 20cos2x Which satisfies y(0) = 1 y'(0) = 0 Homework Equations The Attempt at a Solution

I recently attempted to solve the following: y” + (K/m)y = (Kl^{0}+mg)/m y(0) = l_{0} y(t_{e}) = (K l_{0}+mg)/K The Attempt at a Solution y(t) = -(mg/K)cos{\sqrt{K/m} t} + (mg/K){cos{\sqrt{K/m} t_{e}}/sin{\sqrt{K/m} t_{e}}}*sin{\sqrt{K/m} t} + (K l_{0}+mg)/K which...

I need help. For the following problem, can someone suggest how I should start on this question. I only have one quarter of diff eq classes plus a few classes in Fourier analysis. I'm out of my league. Consider a box with length, width and height given by L. The box encompasses the region...

I want to solve: y(x)''-(\frac{m\pi}{a})^2y(x)=0 With boundary condition y(0)=y(a)=0. First part is very easy using constant coef. which give: y(x)=c_1 cosh(\frac{m\pi}{a}x) + c_2 sinh(\frac{m\pi}{a}x) y(0)=0 \;\Rightarrow\; c_1=0 \;\Rightarrow\; y(x) = c_2 \; sinh(\frac{m\pi}{a}...

Homework Statement Consider the system of coupled second-order differential equations u''-(t+1)(u')^2+2uv-u^3=\cos{t} 2v''+(\sin{t})u'v'-6u=2t+3 with initial conditions u(0)=1, u'(0)=2, v(0)=3, v'(0)=4. Use the second order Runge-Kutta method with h=0.2 and a=2/3, b=1/3, \alpha=\beta=3/2...

So I have never solved a second order NON LINEAR ode before, but my current project has thrown one at me. I am going to use MATLAB to solve it when I have it in the correct state, but at the mo, I can't get it to that... Its three coulped equations, in terms of x,theta and x2. They are in a...

I want to know if there is a general solution to a second order homogeneous differential equation with variable coefficients?

I have the following equation d^2y/dx^2 +4dy/dx +8y = 4sin(2x) - 12cos(2x) y(0)=1 & y'(0)=-6 For the auxillary equation I have (m + 2)^2 = sqrt -4 which gives m=-2-2i & m=-2+2i Which gives y=e^-2x(Ccos(-2x) + Dsin(-2x)) Now to tackle particular integral. Try y=acos(2x) +...

I'm looking at a guide by Texas Instruments on active filter design. In it are the following equations for a second order lowpass filter, verbatim: The coefficient form of the denominator: s^2 + a_1s + a_0 Normalized: P(s) = (\frac{s}{\sqrt{a_0}*\omega_c})^2 + \frac{a_1s}{a_0*\omega_c} + 1...

I'm doing an undergrad research job.. I have encountered the following coupled 2nd order linear ODE with constant coefficients a, b, c, d... \begin{align} \frac{d^2 y_1}{d x^2} + a^2y_1 & = -c y_2 \\ \frac{d^2 y_2}{d x^2} - b^2y_2 & = -d y_1 \end{align} In addition, I...

Homework Statement y''x^{2} + 4xy' -y = ln(x) The Attempt at a Solution -I considered the quadratic characteristic equation, but it won't work because of the x^2 -I also tried variation of parameters. so i have v = y' and v'=y'' but i have no idea what i would sub when I get to y. any...

Homework Statement Solve \frac{d^2 u(x)}{dx^2}=x(1-x) subject to the homogeneous boundary conditions u(0)=0=u(1), using Green's functions. Homework Equations Green's functions... The Attempt at a Solution There are three parts: i - homogeneous eqn: \frac{d^2...

I'm not very experienced on heat laws and devices, other than general thermodynamics. But I am studying 2nd order systems, and the curiosity came up if there is a 2nd order thermo system, since my book only described a 1st order one. I see the thermal capacity as an electronics capacitor...

Homework Statement Find the general and, if possible, particular solutions of the following ordinary differential equations: y''+9y=36sin3x (hint: modification rule for PI) Homework Equations Knowledge of ODE's y = y_{aux}+y_{particular} The Attempt at a Solution I get the compementary...

{\frac {{\it du}}{{\it dx}}}=998\,u+1998\,v {\frac {{\it dv}}{{\it dx}}}=-999\,u-1999\,v u \left( 0 \right) =1 v \left( 0 \right) =0 0<x<10 Second Order Backward Difference formula {\frac {f_{{k-2}}-4\,f_{{k-1}}+3f_{{k}}}{h}} I'm trying solve this numerically in matlab, but can't seem to...

Homework Statement What's the general procedure for solving an i.v. b.v. ode of the form (d^2 T(x))/ (d x^2) = -c * e^T(x) T(+/-1) = 0 T'(0) = 0 where c is a constant Homework Equations i know from ode class that problems like this can usually be evaluated as T'' +...

Homework Statement \frac { d^2 \theta }{d x'^2 } = -y *exp(\theta) eq. 1 mayb be integrated to yield exp(\theta) = \frac {a}{cosh^2(b \frac{+}{-} \sqrt \frac{a*y}{2} * x')} \theta = f(y,x') Homework Equations The Attempt at a Solution the exponent is throwing me off, but i probably...

Homework Statement Let y be the solution of the initial value problem: y'' + 2y' + 2y = 0 , y(0) = 0 , y'(0) = 5 The maximum value of y over 0 less than or equal to x less than infinity is ??. The Attempt at a Solution r = -2 +/- i I solved it: y = c1 e^-2x cos(x) + c2 e^-2x sin(x) y' =...

Homework Statement Find the general soulution to : y'' = sin(2x) and the particular solution that satisfies: y(0) = −1/4, y(pi/4) = pi/2. Homework Equations y = c1y1(x) + c2y2(x) + yp(x) The Attempt at a Solution y'' = sin2x ----> y = -sin(2x)/4 -0.25C1sin(2x) - 0.25C2sin(2x)...

Homework Statement find a general solution to the eq: y''=sin(3t)+4e^t Find a particular solution that satisfies y(0) = 1 y'(1) = 0 Homework Equations The Attempt at a Solution ive figured the general solution to be y(x)= -sin(3t)/9 + 4e^t + c + d And thus y'(x) = -cos(3t)/3...

Hi, I am just looking for clarification whether or not I am doing these problems correctly, here's an example: Homework Statement Find the general solution to x'' -2x' + 5x = 0 Homework Equations Charasteristic polynomial. Quadratic equation. General solution form for complex...

For a second order differential equation, is it necessary to derive a weak form if quadratic interpolation are used?

I'm trying to solve the equation y'' = x^2 * y. This looks like it should be simple, but I don't have mathematica and the only reference I've found calls it a special case of the Emden-Fowler equation and refers to a solution in a book I don't own. Does anyone know the solution to this...

Homework Statement Solve 354y`` −692y` + 235y =0 y(0) = 7 y`(0) = 4 Homework Equations The Attempt at a Solution First I divided the equation by 354 to get y`` - 1.56y` + 0.894y = 0. Then I found the roots of this to be 0.94, repeated twice. For repeated roots the solution looks like y=...

Help solving 2nd order differential equation please While solving for the time it takes an object of mass, m, with initial velocity, v, to compress a spring with spring constant, k to the maximum compression, I came across the following differential equation m(d^{2}x/dt^{2}) = kx - mg I...

Homework Statement \frac{d^2\phi(\eta)}{d\eta^2} = (\eta^2 - K) \phi(\eta) Where K is essentially a constant, K = 2n + 1 (n is an integer). The Attempt at a Solution I don't even know where to begin since \phi is a function of \eta. A push in the right direction would be much...

Homework Statement y'' - 2y'+ 6y = 0 y(0) = 3 y(5) = 7 Find a solution y(t).Homework Equations The Attempt at a Solution I found the characteristic equation: x2 - 9x = 0, which has roots at 0 and 9. Therefore y(t) = C1e0x + C2e9x Using the initial conditions to solve this: 3 = C1 + C2 7 =...

uxx - x2 uyy = 0 (assume x>0) Is there any systematic method (e.g. change of variables) to solve this hyperbolic equation? dy/dx = [B + sqrt(B2 - AC)]/A => dy/dx = x => 2y -x2 = c dy/dx = [B - sqrt(B2 - AC)]/A => dy/dx = -x => 2y + x2 = k So the characteristic curves are 2y -x2 =...

• No ripple can exist in the output, but non-linear phase shift is allowed. • The frequency response must be as close as possible to the ideal filter response. • Signals of frequency 0 ~ 5 KHz are only allowed to pass through the filter with a desired gain of 4dB . Other frequencies should...

Hi~ I'm having trouble with solving a certain differential equation. x2y'' + x y'+(k2x2-1)y = 0 I'm tasked to find a solution that satisfies the boundary conditions: y(0)=0 and y(1)=0 I have tried solving this using the characteristic equation, but i arrived at a solution that is...

when using the power series to solve an ODE, is it always necessary to shift the index to 2 and 1 when taking the second and first derivatives of the power series respectively? i noticed that if i don't shift the index at all and leave them at n=0, it still works out fine? also, how...

The question is If f(x) = 7x^3 + 8x^2 - x + 11, evaluate : a, Integral +1 - -1 f(x) dx b, Integral +1 - -1 f'(x) dx c, Integral +1 - -1 f''(x) dx For a, Just integrate each individual and then input the figures which gave me 1.75x^4 + (8x^3)/3 - 0.5x^2 + 11x Which when I input...

Hi, I am trying to guess the solution for this i am sure the solution involves a ln(x) so that i can reduce the order to find the general solution but i just can't seem to find it... any suggestions ?? \[ (c_{o}+xk)y''+ky'=0\] with ths usual boundary conditions...

I know how to go about solving differential equations of the form y''+q(x)y'+t(x)y = 0 through the methods of finding the characteristic polynomial of the differential equation and solving for the roots, etc. But what I am not clear on is how I would go about solving an equation like this where...

Homework Statement Find General Solution: y"+6y'+9y=e-3x-27x2 Homework Equations The Attempt at a Solution I know you have yh which is the general solution to the left side of the equation set to 0 and then fine the particular solution. When i try to find yp1 I get...

Homework Statement I was curious if anyone could help me prove the equivalence between the two forms of solutions to second order ODEs, one being the linear combination of two solutions and the other being the phase-shifted sin/cos function. Homework Equations...

y''-2y''-3y=3e^2t find the general solution I have tried Ate^t, Ate^2, Ate^3 none have worked they all leave extra variables that don't match up. is there another combination I could try?

Homework Statement Hi, So I'm suppose to solve the following problem: \left.\frac{d^{2}u}{dt^{2}}-4\frac{d^{3}u}{dt dx^{2}}+3\frac{d^{4}u}{dx^{4}}=0 \left.u(x,0) = f(x) \left.\frac{du}{dt}(x,0) = g(x) Homework Equations The Attempt at a Solution First I use Fourier transform on...

Hi, I need some help, I must solve the following nonlinear differential equation, -k1*(c'') = -k2*(c^0.5) - u*(c') subject to the bc, u*(c - 0.5) = k1*(c') where k1, k2, and u are constants, thanks

Hi, Does anyone knows how to solve this 2nd order non linear differential equation with exponential components? d"V/dx" = A*exp(-B*V)-C*exp(B*V) where A, B, C are constants. Thanks