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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\int \frac{2 x + 1}{x ^{2} + 2 x + 10} d x

x \to 2 lim (x^{2} - 3 x + 1)

x \to 2 lim ([1 + f (x)]^{2})

\frac{\partial}{\partial x} (\frac{2 x}{z - y})

\int_{0}^{\frac{π}{3}} 10 sec^{2} (x) d x

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