# Linear ODE solutions

1. Mar 11, 2012

### physicsjock

Hey,

I have been trying to work out how to solve this example question I found in a recommended text,

http://img715.imageshack.us/img715/5052/asdavm.jpg [Broken]

Everywhere I've been reading starts with since y=eta(x) is a particular solution then y=eta(x) + u is a general solution, but the question doesn't state eta(x) as a particular solution, is that a problem?

Anyway in this question is the way to go simply subbing in y = eta + 1/si then noting that all the lone eta components cancel since they are a solution themselves.

But when I do that,

I end up with something like

$\frac{dx}{d\Psi }=\left[ p(x)+2q(x)\eta (x) \right]\Psi (x)+\frac{q(x)}{{{\Psi }^{2}}(x)}$

and I can't rearrange it to form the equation which si solves,

any idea on what i've done wrong?

Last edited by a moderator: May 5, 2017
2. Mar 11, 2012

### tiny-tim

hey physicsjock!

where did that dx/dψ come from?

it should be -(1/ψ2)dψ/dx

(and then you'll be able to multiply throughout by ψ2)

3. Mar 11, 2012

### physicsjock

ahah what a silly mistake I made!

Thanks heaps!