What is the solution for 9x^2y^'=y^'+5xe^{-y} ?

The solution for 9x^2y^'=y^'+5xe^{-y} is y=ln(5/18 ln(9x^2-1)+c_{1})

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9x^2y^'=y^'+5xe^{-y}

9 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}

y = ln (\frac{5}{18} ln (9 x^{2} - 1) + c_{1})

Solution steps

9 x^{2} y^{'} (x) = y^{'} (x) + 5 x e^{- y}

Solve separable ODE:

y = ln (\frac{5}{18} ln (9 x^{2} - 1) + c_{1})

y = ln (\frac{5}{18} ln (9 x^{2} - 1) + c_{1})

\frac{d y}{d x} = x \cdot e^{- 2 x}

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

\frac{d ^{2} y}{d x ^{2}} + y = csc (x)

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

y = x^{2}, (0, 4)

What is the solution for 9x^2y^'=y^'+5xe^{-y} ?
The solution for 9x^2y^'=y^'+5xe^{-y} is y=ln(5/18 ln(9x^2-1)+c_{1})