By tracing a series of slopes, you should predict that the original function is cubic.

Separate the variables so that x-values are on one side of the equal sign and y-values are on the other side.

Integrate both sides of the equation.

Solve for y... Did you get a cubic function, as predicted?
Note: C₁ + C₂ = C₃, or just C.

2dy = x²dx

$\int 2dy=\int x^{2}dx$

$2y+C_{1}=\frac{x^{3}}{3}+C_{2}$