What is the solution for e^{x+y}(dy)/(dx)=2x+xe^y ?

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

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e^{x+y}(dy)/(dx)=2x+xe^y

e^{x + y} \frac{d y}{d x} = 2 x + x e^{y}

y = ln (e^{- x e^{- x} - e^{- x} + c_{1}} - 2)

Solution steps

e^{x + y} \frac{d y}{d x} = 2 x + x e^{y}

Solve separable ODE:

y = ln (e^{- x e^{- x} - e^{- x} + c_{1}} - 2)

y = ln (e^{- x e^{- x} - e^{- x} + c_{1}} - 2)

\frac{125}{x ^{2} + 25}

\frac{d}{d x} (x^{4} - 4 x^{2} + 2)

\frac{\partial}{\partial x} (- (x^{2} + y^{2}))

x \to 1 - lim (2 x + 2)

- 3 x^{2} - 8 x

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