Hi, i need to know how to solve this ODE. Please see the attachment. The solution is 2logx but i don't know to get it. Any help would be much appreciated. thanks

Results 1 to 3 of 3

- Jan 16th 2009, 11:27 AM #1

- Joined
- Mar 2008
- Posts
- 26

- Jan 16th 2009, 11:35 AM #2

- Joined
- Dec 2008
- From
- Scotland
- Posts
- 901

Let $\displaystyle u = \frac{dF}{dx} $. This should reduce it to a 1st order ODE of the form:

$\displaystyle \frac{1}{2}x^2 \frac{du}{dx} +xu =1 $

Which can be written:

$\displaystyle \frac{du}{dx} +\frac{2}{x}u =\frac{2}{x^2} $

You can solve this for $\displaystyle u $ using an integrating factor! Giving a solution of the form:

$\displaystyle u = f(x) + C $

Then remember that:

$\displaystyle F = \int u dx $

Also, can I ask why you used $\displaystyle \partial$ instead of $\displaystyle d$ if it's an ODE? $\displaystyle \partial$ is reserved for PDEs, or Partial Differential Equations... ie... Differential Equations of functions of more than 1 variable.

- Jan 16th 2009, 01:42 PM #3

- Joined
- Mar 2008
- Posts
- 26