Variation of parameters Definition and 116 Threads

Well, i really i am pissed at the moment because of this. I have been trying to figure out if there is a proof/justifaction for the method of variation of parameters and have had absolutly no luck. I have searched the internet and almost every differential equation books in my university library...

Homework Statement x^2y''-2xy'+2y=x^3cosx Find a general solution by using variation of parameters 2. The attempt at a solution I already solved this one, but I have 4 questions: 1. I found the solutions x and x^2 to the homogeneous equation by inspection. Is this the only way to...

Homework Statement Given that y=x^2 is a solution to the differential equation: (x^2)y'' + 2xy' - 6y = 0 <--- Eq.(1) find the general solution of the differential equation (x^2)y'' + 2xy' - 6y = 10(x^7) + 15(x^2) <--- Eq.(2) Hence write...

Hi i need to use Variation of Parameters to solve this ODE x^2 y'' - 2xy' + 2y = x^(9/2) So far I was thinking to use Euler's Equation and I really don't know if it will work please help me out with a hint. THanks.

Nonhomogenous LODE (Higher Order) - Method of Variation of Parameters x^3y''' + x^2y'' - 2xy' + 2y = x^3log(x) y(1) = \frac{10}{32} y'(1) = -\frac{24}{32} y''(1) = -\frac{11}{16} I know that \inline y = y_h + y_p and that I probably should use the method of variation...

Given that http://forums.cramster.com/Answer-Board/Image/cramster-equation-200641003458632802260985487500893.gif is the complementary function for the differential equation http://forums.cramster.com/Answer-Board/Image/cramster-equation-200641003635632802261951581250765.gif use the variation...

Use the method of variation of parameters to find a particular solution of http://forums.cramster.com/Answer-Board/Image/cramster-equation-2006491914366328020687673812501253.gif ok i know first i do...

I'm not currently in a class, but I'm doing this for fun.. but technically I would still call it coursework, so I'm posting it here.. I'm studying Redheffer/Sokolnikoff's Mathmatics of Modern Engineering.. and I find a problem on page 75, use the method of variation of parameters to find the...

OKay everyone, this is a big f'ing problem (to me anyways) and its only worth 1 point! But I'm doing it anyways. So here was my attempt, everything seems to be working out like it should but look at what u1 came out too, what am i going to do with that mess? Also do u see any mistakes...

i'm confused about that method: 1) when proving that method works, why do you have to make u and v satisfy the 2nd condition u`y1+v`y2=0 2) when you're integrating to find yp, why do you leave out the constant that results from the integration?

I know how to solve the following ODE with variation of parameters: y''+4y=4\sec{\left(2t\right)}. Is there any way to solve this with undetermined coefficients? So far I have tried Yp=Acos(2t)+Bsin(2t), but that didn't work. Thanks for the help.

solve using method of variation of parameters y''-y = 2/(1+e^x) y'' ==> second order

I have been trying to get this for a while and can't figure it out: if a fundamental matrix of the system x' = Ax is X(t) \left(\begin{array}{cc}e^t&0\\0&e^{-t}\end{array}\right) find a particular solution yp(t) of x' = Ax + [e^t, 2]^{transpose} such that yp(0) = 0 So, I got u(t) =...

I need to solve this D.E. x^2y''-xy' + y = x^3 i'm supposed to use the variation of parameters technique. in that technique i need to get a coeffecient of 1 in the first postion of y'' and then sove the homogenous D.E. y''-\frac{y'}{x} +\frac{y}{x^2}=0 the above leads to...

Hello, I'm trying to understand this concept. Jere's the problem I'm doing. I have to find the general solution for: y'' + 36y = -4xsin(6x) So you then solve for your characteristic equation and get lamda = +/- 6 so y1 = e^-6x and y2 = e^6x You get your matrix for w, w1, and w2. w =...

the problem is fin the general solution of the differential eq : y''+y=2sect + 3 (-pi/2 < t < pi/2) using variation of parameters. I just needed a check to make sure my answer was correct. r^2+1 = 0 r= -i r= i y1= cost y2= sint g(t)= 2sect+ 3 y(t) = c1cost + c2sint + Y(t)...