What is the solution for 4x^2*y^'=y^'+9x*e^{-y} ?

The solution for 4x^2*y^'=y^'+9x*e^{-y} is y=ln(9/8 ln(4x^2-1)+c_{1})

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4x^2y^'=y^'+9xe^{-y}

4 x^{2} \cdot y^{^{'}} = y^{^{'}} + 9 x \cdot e^{- y}

y = ln (\frac{9}{8} ln (4 x^{2} - 1) + c_{1})

Solution steps

4 x^{2} \cdot y^{'} (x) = y^{'} (x) + 9 x \cdot e^{- y}

Solve separable ODE:

y = ln (\frac{9}{8} ln (4 x^{2} - 1) + c_{1})

y = ln (\frac{9}{8} ln (4 x^{2} - 1) + c_{1})

\frac{\partial}{\partial x} (x^{13})

x^{2} - 5 x + 5

\frac{\partial}{\partial x} (y cos (x^{2} + y^{2}))

\frac{d}{d x} (\frac{- 1}{1 - x})

\frac{d}{d x} (\frac{x}{1 + 1 - x ^{2}})

What is the solution for 4x^2*y^'=y^'+9x*e^{-y} ?
The solution for 4x^2*y^'=y^'+9x*e^{-y} is y=ln(9/8 ln(4x^2-1)+c_{1})