What is the solution for (e^x+1)^2e^{-y}dx+(e^x+1)^3e^{-x}dy=0 ?

The solution for (e^x+1)^2e^{-y}dx+(e^x+1)^3e^{-x}dy=0 is y=ln(-ln(e^x+1)+c_{1})

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(e^x+1)^2e^{-y}dx+(e^x+1)^3e^{-x}dy=0

(e^{x} + 1)^{2} e^{- y} d x + (e^{x} + 1)^{3} e^{- x} d y = 0

y = ln (- ln (e^{x} + 1) + c_{1})

Solution steps

(e^{x} + 1)^{2} e^{- y} d x + (e^{x} + 1)^{3} e^{- x} d y = 0

Solve separable ODE:

y = ln (- ln (e^{x} + 1) + c_{1})

y = ln (- ln (e^{x} + 1) + c_{1})

\frac{d y}{d t} + 2 y = 4

y^{^{'}} = y^{2} e^{- x}

y^{^{'}} = y t^{2} - 1.1 y, y (0) = 1

y^{^{'}} = \frac{3 t ^{2}}{4 + 2 y}

y^{^{'}} = y x^{2} - 1.1 y

What is the solution for (e^x+1)^2e^{-y}dx+(e^x+1)^3e^{-x}dy=0 ?
The solution for (e^x+1)^2e^{-y}dx+(e^x+1)^3e^{-x}dy=0 is y=ln(-ln(e^x+1)+c_{1})