# Seperable Differential EQ

• Apr 9th 2009, 12:11 PM
xwanderingpoetx
Seperable Differential EQ
The question is

$\frac{du}{dr} = \frac {1+\sqrt{r}}{1+\sqrt{u}}$

And I am supposed to solve for u.

$u + \frac{2\sqrt{u^3}}{3} = r + \frac{2\sqrt{r^3}}{3} + C$

Is there a way I can solve for u?
• Apr 9th 2009, 12:29 PM
Moo
Hello,

Is there an initial condition so that you can get C ?

Because if C is 0, I have this factorisation :

$(\sqrt{u}-\sqrt{r})\left(\frac 23 \cdot u+\frac 23 \sqrt{ur}+\frac 23 \cdot r+\sqrt{u}+\sqrt{r}\right)=0$

Since you talked about $\sqrt{r}$ and $\sqrt{u}$, we can assume that u and r are positive.

Thus the solutions are : u=r, or u=r=0 (for the second term, because it's always $\geq 0$)
• Apr 9th 2009, 12:34 PM
xwanderingpoetx
$C$ is just the arbitrary constant associated with the integration. But it isn't given a value so it needs to be in the final equation.