What is the solution for 6x^2y^'=y^'+2xe^{-y} ?

The solution for 6x^2y^'=y^'+2xe^{-y} is y=ln(1/6 ln(6x^2-1)+c_{1})

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6x^2y^'=y^'+2xe^{-y}

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

y = ln (\frac{1}{6} ln (6 x^{2} - 1) + c_{1})

Solution steps

6 x^{2} y^{'} (x) = y^{'} (x) + 2 x e^{- y}

Solve separable ODE:

y = ln (\frac{1}{6} ln (6 x^{2} - 1) + c_{1})

y = ln (\frac{1}{6} ln (6 x^{2} - 1) + c_{1})

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What is the solution for 6x^2y^'=y^'+2xe^{-y} ?
The solution for 6x^2y^'=y^'+2xe^{-y} is y=ln(1/6 ln(6x^2-1)+c_{1})