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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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