Question

dy/dx=(8x^(3))*e^(-2y) ; y(1)=0

Answer 1

Separable
\[\Large \frac{dy}{dx}=(8x^{3})e^{-2y} \\ \\ \Large \int\limits \frac{1}{e^{-2y}}dy=8\int\limits x^3dx\]
\[\Large \int\limits\limits e^{2y}dy=8\int\limits\limits x^3dx\]
Power rule for both integral

Answer 2

Thanks