Second order Definition and 570 Threads

Ly ≡ (x +1)^2y′′− 4(x +1)y′+6y =0 given y[1]=(x+1)^2 is a solution, use the ansatz y2(x)= u(x)(x+1)2 to reduce the order of the differential equation and find a second independent solution y2 how to reduce !? and i can't find u ...can't solve (x+1)^2u''+6u=0 please help! thx!

Hi, I just had my ordinary differential equation final exam today (summer class), the exam was fine. We had a bonus question though, it was a nonlinear second order differential equation, we didn't learn anything about those except for one existence and uniqueness theorem. I am curious if I got...

Homework Statement Substitute p = \frac{dx}{dt} to solve x\prime\prime + \omega^2x = 0 Homework Equations \frac{dp}{dx} = v + x\frac{dv}{dx} v = \frac{p}{x} The Attempt at a Solution p = \frac{dx}{dt}, \frac{dp}{dt} = \frac{d^2x}{dt^2} \frac{dp}{dt} = \frac{dp}{dx}\frac{dx}{dt} =...

Homework Statement It will be great if someone could show me some options: I need to prove the following: A particle of mass m is attracted toward a fixed point O (the origin) with a force proportional to its instantaneous distance from O raised to a positive integer power, i.e...

Hi, I am sure I have mistaken my DE setup or my initial conditions assumption. Homework Statement http://ivila.net/E8.png R1 will be the middle Resistor R2 the top one. Homework Equations i1' + R1/L i1 = R1/L i2 i2(R1+R2)*1/(R1) + 1/(R1*C)*integral(i2)=i1 The Attempt at a...

second order nonlinear ODE -- not autonomous This equation has arisen from a steady state problem of diffusion with nonlinear reaction: (dependent var=c; independent variable=x) c'' = ko + k1 c + k2 c^2 + k3 c x ko, etc are constants. I can obtain a solution if I drop the last term...

Homework Statement Solve the following equation f'' - 3f' + 2f = 3 For f(0) = 0,\ and\ f'(0) = 1 Homework Equations None. The Attempt at a Solution Ok, so, I know how to solve inhomogeneous ODEs when it's on this form af'' + bf' + cf = g Where g is a given function. But how do I...

Homework Statement (1+x2)y'' - 4xy' + 6y = 0 Homework Equations I'm going to assume y can be written as [n=0 to ∞] ∑anxn The Attempt at a Solution y = [n=0 to ∞] ∑anxn ----> y' = [n=0 to ∞] ∑(n+1)an+1xn ----> y'' = [n=0 to ∞] ∑(n+2)(n+1)an+2xn ---->...

show that y1(x) = e^(2+i)x and y2(x) = e^(2-i)x, i=sqrt(-1) are two linearly independent functions hence obtain a second order linear differential equation with constant coefficients each that y1(x) and y2(x) are its two fundamental solutions. my attempt : for the first part, I use the...

Hello All, I am stuck on the following question. Can you please help to find the solutions Using the complementary function and particular integral method, find the solution of the diffential equation which satisfies y(0) = 1 and y'(0) = 0. y'' + 3y' + 2y = 20cos2x and then can you...

ok, for 2nd order differential equations, if we have repeat roots, like for example y" +4y = cos2x , we would have repeat roots +2i,-2i. so how do we try for the particular solution? i tried Acos2x + Bsin2x, it all canceled out. i tried (Ax+B)cos2x + (Cx+D)sin2x it all canceled out too then...

I need to solve the following system of differential equations: \frac{\partial^2 y}{\partial t^2} + A\frac{\partial y}{\partial t} - B \frac{\partial^2 y}{\partial z^2} = Cq \frac{\partial^2 q}{\partial t^2} + D\frac{\partial q}{\partial t} + q = E\frac{\partial^2 y}{\partial t^2}...

Homework Statement if given the general solution to a differential equation y(t)=a cos t + b sin t + ((cos wt)/1-w^2), Find out how long it takes the solution to approach the steady state solution. original second order differential equation: y'' + y = cos wt such that 0 < w < 10...

my question is: what is the general solution of this system of coupled diff. equations: f ''i = Cijfj C is a matrix, fj(z) are functions dependent of z.

Homework Statement a) ẍ + 5ẋ + 4x = 0 x(0) = 0, ẋ(0)=1 What type of damping? b) ẍ + x = cos(t) x(0) = 0, ẋ(0)= 1 What type of motion? The Attempt at a Solution a) Let x = R Eᴿᵀ R = -4 R = -1 x(t) = CE**-4T + DE**-t C + D = 0 -4C - D = 1 C = 1/5 D = 1/5 And it is...

Hi everybody, I'm reading about sigma delta adc, the base theory. I've read about the first order modulator and now the second order, but I have a problem (maybe stupid) with a phrase of my book (Data Converters by F.Maloberti), when he describe the 'passage' from first order to second order...

How, if possible, could I solve the equation: x''x=((x')^2)/2? Thanks.

Homework Statement Please see attachment for block diagram of the system. Starting with the block diagram given in Figure 2 derive an expression for the overall transfer function of the system, where Gc(s) is in the form given by Eq. (1). Show that the system is a Second Order system...

Homework Statement y''[x] = y'[x] + x Homework Equations We were taught two special types of second order diff. equations: Type 1: Supposed to be when x is missing v = y'[x] v'[x] = y''[x] Type 2: Supposed to be when y is missing v = y'[x] v v'[x] = y''[x] The Attempt at...

Hello, I was wondering if anyone could shed some light upon solving this: s(x)'' = (a b s(x)) / ||s(x)||^3 Where s is a n dimensional vector, || || is operation finding the magnitude and a and b are constants. Is this solveable or will I have to use alternative numerical methods?

Out of boredom* I derived some simplified equations to describe the dynamics of a pneumatic gun. These equations are extremely simplified, but they should provide some insight into the system that my numerical models can't. This system had one non-linear equation that could be rewritten as the...

Find k: 20\frac{d^2x}{dt^2} + \frac{dx}{dt} + kx = 0 when t = 0 - x = 1 - dx/dt = 1 My attempt at this in maxima: (%i1) 20*'diff( 'diff(x, t), t) + 'diff(x, t) + k*x = 0; 2 d x dx (%o1) 20 --- + -- +...

I want to write a program in C that's going to solve 3 second order differential equations, and I have little to no experience in solving differential equations in C (however, I know C well enough). I'm having a bit of trouble. First of all, I don't really know what method I'm going to use to...

Homework Statement What is the general solution to y'' - 2(y')^2 = 0 ? Homework Equations The Attempt at a Solution Let u = y ' u ' - 2u^2 = 0 u ' = 2u^2 u = (2 / 3)u^3 + C This cannot be solved using separation of variables, what is done?

Homework Statement Find if it is true that the general solution to : y'' - y' = 0, where y(x), can be written as : y(x) = c1 cosh(x) + c2 sinh(x), where c1 and c2 are real arbitrary constants. Homework Equations differential equation solving The Attempt at a Solution I just...

Homework Statement I have differential equation;] this is equation from central force thing in Lagrange mechanics, you know, you know, its second order hahaha:D y^3y^{\prime\prime}=ay+b Homework Equations I will using method of making a first degree of this equation The Attempt at a...

Hi guys, I really have no idea how to approach finding the particular integral for, say: f'' + 5f' + f= e^x sinx Could anyone help me? And for future reference how do you go about finding the PI for any combination of polynomials/exponentials/sinusoidals? Thanks in advance for the help!

Hi, i have the following non-homo differential equation. y^{\prime\prime}+4y = 2~cos~x + 3x~sin~x \begin{cases} y(0) = 1 \\ y^{\prime}(0) = 2 \end{cases} Since there is a 3x term in front of sin x. What is the form of the solution for this problem? if it hadn't been there it...

Is there any physical reason why second order approximation to ground state in time independent perturbation theory is always negative. I know how to prove it mathematicly but I wonder whether one may justify it using only physical arguments.

Hello, I hope I am writing to right part of a forum... I made a differential equation when I was solving my problem, but unfortunately I am not capable of solving such equation since I am only 12th grader. Or maybe it is not possible to solve it at all...

How do i solve the following equation? u= L*(d^2i/dt)+ (1/c)*i r* (di/dt)L= 1,4 mF C= 0,31 H R= 1000 ohm Well i have so far found the auxiliary equation: 0,31*r^2 + 1000*r + 1/(1,4*10^-6)=0 And the discriminant is found to be 114286. This makes the form of the solution: Y=c1*e^r1x +...

I've created a second order homogeneous equation from my orginal data m(d^2x/dt^2) + kx = 0 how can I turn it into a expression of displacement relevant to time?

Homework Statement I have a RLC circuit in series. I am trying to find the current i(t) passing through this RCL circuit. When solving the RCL circuit, it happened to be critically damped. And simplified i ended up with: i(t) = A2te-20t Where i need to find what is the cosntant A2 Homework...

Homework Statement a and b are functions of z: a=a(z); b=b(z) I want to calculate the second order partial derivative operator on z Homework Equations Using the chain rule: \frac{\partial}{\partial z}=\frac{\partial a}{\partial z}\frac{\partial}{\partial a}+\frac{\partial...

Homework Statement Find a third degree polynomial approximation for the general solution to the differential equation: \frac{d^{2}y}{dt^{2}} +3\frac{dy}{dt}+2y= ln(t+1) Homework Equations Power series expansion for ln(t+1) The Attempt at a Solution The system to the...

Homework Statement Consider the differential equation \bold{x}'=\left[ \begin{array}{cc} -1 & 2 \\ -1 & -3 \end{array} \right]\bold{x}, with \bold{x}(0)=\left[ \begin{array}{c} 1 \\ 1 \end{array} \right] Solve the differential equation where \bold{x}=\left[ \begin{array}{c} x(t) \\ y(t)...

I understand how to solve a normal second order linear equation, but this question in the homework is a bit more theoretical and I'm a bit confused. "Suppose y[SIZE="1"]1(t) and y[SIZE="1"]2(t) are solutions of y'' + py' + qy = 0 Verify that y(t) = k[SIZE="1"]1y[SIZE="1"]1(t) +...

Hello sorry for my English, i know its bad;) I have a simultaneous differential equation of second order (moving of point mass around point mass M in beginning of cartesian system) \begin{cases}\frac{\mbox{d}^2x}{\mbox{d}t^2}=-GMx\left(x^2+y^2\right)^{-\frac{3}{2}}\\...

For my thesis I need to solve many differential equations non linear, second order by using maple... For example figure adjoint using dsolve command, the solutions are very extensives and very bad. there is a suggest for to solve the differential equations by using maple? there is some...

A Nonlinear Second Order Differential Equation Problem: very frustrating please help! Hello, I am a first year engineering undergraduate student, and this is my question. Homework Statement A dust particle of negligible mass starts to fall, t=0, under the influence of gravitational force...

Hi, I came across the following differential equation: \sqrt{1+(y')^2}=\frac{d}{dx}\left(y\frac{y'}{\sqrt{1+(y')^2}}\right) I found possible solutions: y\left(x\right)=cosh(x+C_{1}). However, this is a second order ODE so there exist a more general solution, with 2 freedom degrees...

hello i need some help here! solve: x''+3x'+2x=1/(1+e^t) well ok the homogeneous solution is c1*e^t+c2*e^2t but how to determine the particular solution Xp!

Okay, so my problem lies within taking the second derivative of a change of variable equation. w = f(x,y); x = u + v, y = u - v so far I have the first derivative: dw/dx = (dw/dv)(dv/dx) + (dw/du)(du/dx) = (d/dv + d/du)w Now I'm having problems in finding my second derivative...

Homework Statement Find the general solution to y'' + y = sec3(x) The Attempt at a Solution Well I can get the characteristic equation: r2 + 1 = 0 r = +-i Then the homogeneous solution is yh = C1excos(x) + C2exsin(x) And I know y = yh + yp but how do I get yp? I've never...

Hi everyone, I am studying to write my final Mechanical Engineering Prep Exam and have come across some problems that I am having a hard time figuring out. I have managed to figure out how to use the Euler-Cauchy Equations to solve problems of the form: x2y" + axy' + by = 0 where a and b...

Just wondering does it matter which coupled differential equation you solve first ( i terms of time)? normally i just solve the first equation, so far all our tutorial question involved finding solutions to second order equations that have 2 distinct roots ( for the auxilliary equation)...

Hi, I have a second order differential equation but I do not know how to solve it. \frac{d^2Q}{dn^2}\left -A(B-n\right)\frac{dQ}{dn}+ \left(A + \frac{C}{n}\right)Q = 0 Appreciate if anyone could help me on this. Thank you

Hey Guys, I've been banging my head with this one for a few days now. I've done (a) and (b) but I'm yet to do (c) if someone could complete this for me or help me along the way that would be greatly appreciated. Thanks heaps!

When we write down a Lagragian for a quantum field theory, it is said that it should not depend on the second and higher order time and space derivatives of \phi, because we want the equation of motion(EOM) to be at most second order. Why is it so important. What trouble will a higher order EOM...

hi, everybody i got for homework a pendulum on a cart. i solved the system and got two equations. (m+M)x'' + M L theta'' = F x'' + L theta'' + g* theta = 0 F = 1000 N, m = 500 kg, M = 1250 kg, l = 10m i know how to put them in state space and solve them with SS block in...