Question

Separation of variables. Differential equation.

Answer 1

Uhm divide both sides by y^3?

Answer 2

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Answer 3

\(\large\color{black}{ \displaystyle xy^3~dx=-(y+1)e^{-x}dy }\)

\(\large\color{black}{ \displaystyle e^{x}xy^3~dx=-(y+1)dy }\)

\(\large\color{black}{ \displaystyle e^{x}x~dx=(-(y+1)/y^3)dy }\)

to be technical,

\(\large\color{black}{ \displaystyle e^{x}x=(-(y+1)/y^3)\frac{dy}{dx} }\)

and then integrate both sides with respect to x