What is the solution for (dy)/(dx)=xe^{-y}+10e^{-y} ?

The solution for (dy)/(dx)=xe^{-y}+10e^{-y} is y=ln((x^2)/2+10x+c_{1})

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(dy)/(dx)=xe^{-y}+10e^{-y}

\frac{d y}{d x} = x e^{- y} + 10 e^{- y}

y = ln (\frac{x ^{2}}{2} + 10 x + c_{1})

Solution steps

\frac{d y}{d x} = x e^{- y} + 10 e^{- y}

Solve separable ODE:

y = ln (\frac{x ^{2}}{2} + 10 x + c_{1})

y = ln (\frac{x ^{2}}{2} + 10 x + c_{1})

What is the solution for (dy)/(dx)=xe^{-y}+10e^{-y} ?
The solution for (dy)/(dx)=xe^{-y}+10e^{-y} is y=ln((x^2)/2+10x+c_{1})