Answer
See below
Work Step by Step
Given: $y'=2xy$
Rewrite as: $\frac{dy}{dx}=2xy\\\rightarrow \frac{dy}{y}=2xdx$
Integrate both sides:
$\int \frac{dy}{dx}=\int 2xdx\\
\rightarrow \ln(y)=x^2+c\\
\rightarrow y=e^{x^2+c}$
where $c_1=-2\\c_2=-1\\c_3=1\\c_4=2$
