The question is
$\displaystyle \frac{du}{dr} = \frac {1+\sqrt{r}}{1+\sqrt{u}} $
And I am supposed to solve for u.
The answer I got was
$\displaystyle u + \frac{2\sqrt{u^3}}{3} = r + \frac{2\sqrt{r^3}}{3} + C$
Is there a way I can solve for u?
The question is
$\displaystyle \frac{du}{dr} = \frac {1+\sqrt{r}}{1+\sqrt{u}} $
And I am supposed to solve for u.
The answer I got was
$\displaystyle u + \frac{2\sqrt{u^3}}{3} = r + \frac{2\sqrt{r^3}}{3} + C$
Is there a way I can solve for u?
Hello,
Is there an initial condition so that you can get C ?
Because if C is 0, I have this factorisation :
$\displaystyle (\sqrt{u}-\sqrt{r})\left(\frac 23 \cdot u+\frac 23 \sqrt{ur}+\frac 23 \cdot r+\sqrt{u}+\sqrt{r}\right)=0$
Since you talked about $\displaystyle \sqrt{r}$ and $\displaystyle \sqrt{u}$, 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 $\displaystyle \geq 0$)