Solve the differential equation - getting weird answer

Question

I need to solve this differential equation: $$\frac{du}{dr}=\frac{4+\sqrt{r}}{2+\sqrt{u}}$$

I did it and got $$u=\frac{2r^{\left(\frac{3}{2}\right)}}{3\sqrt{u}+2}+\frac{4r}{\sqrt{u}+2}+C$$ but my homework system is marking this as wrong. Why is that?

Answer 1

you must write $$(2+\sqrt{u})du=(4+\sqrt{r})dr$$ and integrate this! the solution should be $$4\,r+2/3\,{r}^{3/2}-2\,u \left( r \right) -2/3\, \left( u \left( r \right) \right) ^{3/2}+{\it \_C1}=0 $$

Answer 2

Just a hint

$$\frac{du}{dr}=\frac{4+\sqrt{r}}{2+\sqrt{u}}$$ $$(2+\sqrt{u})du=(4+\sqrt{r})dr$$ $$\int(2+\sqrt{u})du=\int(4+\sqrt{r})dr$$ $$2u+\frac 23 u^{3/2}+K=\int(4+\sqrt{r})dr$$ $$..............$$ Do the same for the right side of the equation