## Calculus 10th Edition

$y$ = $\frac{2}{5}x^{\frac{5}{2}} + C$
$\frac{dy}{dx}$ = $x^{\frac{3}{2}}$ 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.