What is the solution for 6x^2y^'=y^'+8xe^{-y} ?

The solution for 6x^2y^'=y^'+8xe^{-y} is y=ln(2/3 ln(6x^2-1)+c_{1})

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6x^2y^'=y^'+8xe^{-y}

6 x^{2} y^{^{'}} = y^{^{'}} + 8 x e^{- y}

y = ln (\frac{2}{3} ln (6 x^{2} - 1) + c_{1})

Solution steps

6 x^{2} y^{'} (x) = y^{'} (x) + 8 x e^{- y}

Solve separable ODE:

y = ln (\frac{2}{3} ln (6 x^{2} - 1) + c_{1})

y = ln (\frac{2}{3} ln (6 x^{2} - 1) + c_{1})

\int \frac{4 x ^{2} + 4 x - 4}{x ^{3} + x ^{2} - x - 1} d x

\frac{\partial}{\partial y} (2 x z^{3} e^{y^{2}})

x, at x = 1

\int x (x - 3) d x

What is the solution for 6x^2y^'=y^'+8xe^{-y} ?
The solution for 6x^2y^'=y^'+8xe^{-y} is y=ln(2/3 ln(6x^2-1)+c_{1})