Answer
$ y $ = $ \frac{2}{5}x^{\frac{5}{2}} + C $
Work Step by Step
$\frac{dy}{dx} $ = $ x^{\frac{3}{2}}$
To get the original equation, we have to integrate the aforementioned differential equation.
$y=\int dy=\int x^{\frac{3}{2}} dx$
= $\frac{x^{{\frac{3}{2}}+1}}{{\frac{3}{2}}+1} + C $
= $ \frac{x^{\frac{5}{2}}}{\frac{5}{2}} + C $
= $ \frac{2x^{\frac{5}{2}}}{5} + C $
= $ \frac{2}{5}x^{\frac{5}{2}} + C $
Hence, $ y $ = $ \frac{2}{5}x^{\frac{5}{2}} + C $
The result checks out by differentiation.
