# How do you find the general solution of the differential equation dy/dx=x^(3/2)?

Dec 28, 2016

Solve for $\mathrm{dy}$.

$\mathrm{dy} = {x}^{\frac{3}{2}} \mathrm{dx}$

Integrate both sides.

$\int \left(\mathrm{dy}\right) = \int \left({x}^{\frac{3}{2}}\right) \mathrm{dx}$

Use the rule $\int \left({x}^{n}\right) \mathrm{dx} = \frac{{x}^{n + 1}}{n + 1} + C$ to solve.

$y = {x}^{\frac{5}{2}} / \left(\frac{5}{2}\right) + C$

$y = \frac{2}{5} {x}^{\frac{5}{2}} + C$

Hopefully this helps!