# Thread: Rearranging to get a linear differential

1. ## Rearranging to get a linear differential

Hi

I have the following value problem :

du/dx = xu

So i rearranged this to become:

du/dx * 1* 1/u = x

I there for concluded:
g(x) = 1 and h(x) = x

I then did this calculation:

The book's solutions how ever gives a different answer since it chose different values for g(x) and h(x). I am wondering if mine is still valid or have i done it wrong? Does u have to be u^1 and nothing else for this to work ?

This is the books solution:

2. ## Re: Rearranging to get a linear differential

The form of a first order linear differential equation is

$u^\prime + g(x)u=h(x)$

there is no $\dfrac 1 u$ term

3. ## Re: Rearranging to get a linear differential

if a differential equation is not "linear" to begin with, no "rearranging" will make it linear!

4. ## Re: Rearranging to get a linear differential

Oops. This post added nothing useful.