Question

I need help with some separable equations!!

Answer 1

\[dy/dx=8e ^{4x}(1+y^2)\]

Answer 2

$$\begin{align*}
\frac{dy}{dx}&=8e^{4x}(1+y^2)\\
\frac{1}{(1+y^2)}dy&=8e^{4x}dx\\
\int\frac{1}{(1+y^2)}dy&=\int8e^{4x}dx\\
\tan^{-1}y&=2e^{4x}\\
y&=\tan(2e^{4x})

\end{align*}$$