## Differential Equations and Linear Algebra (4th Edition)

$ln|y|=x^2+C$
Multiply both sides of the equation by $\frac{dx}{y}$. $$(\frac{dx}{y})(\frac{dy}{dx}=2xy)$$ $$\frac{dy}{y}=2xdx$$ Since each side is in terms of one variable, you can integrate. $$\int \frac{dy}{y}=\int 2x dx$$ $$ln|y|=x^2+C$$