# Homework Help: Variation of parameters problem, very BIG, but i think i'm right so far! Diff EQ

1. Feb 20, 2006

### mr_coffee

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? Thanks!
http://img86.imageshack.us/img86/6803/lastscan0rh.jpg [Broken]
http://img86.imageshack.us/img86/2782/lastscan22bs.jpg [Broken]

Last edited by a moderator: May 2, 2017
2. Feb 20, 2006

### quasar987

That IS a lot of work. Are you sure that's how you're expected to solve these problem? Our friend Lagrange cooked up a crispy formula just for these occasions. It says that if $y_1(t)$ and $y_2(t)$ are linearly independant solution to the homogeneous equation y'' + p(t)y' + q(t)y = 0, then a particular solution to the inhomogeneous equation y'' + p(t)y' + q(t)y=g(t) is

$$Y(t) = -y_1 \int \frac{y_2 g}{W(y_1,y_2)}dt + y_2\int\frac{y_1 g}{W(y1,y_2)}dt$$