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

2. Originally Posted by mbbx5va2
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
Let $u = \frac{dF}{dx}$. This should reduce it to a 1st order ODE of the form:

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

Which can be written:

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

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

$u = f(x) + C$

Then remember that:

$F = \int u dx$

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

3. Sorry yes your right about the notation - i made a mistake. Thanks for the help i've managed to solve it.