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

The solution for 5x^2y^'=y^'+9xe^{-y} is y=ln(9/10 ln(5x^2-1)+c_{1})

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

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

y = ln (\frac{9}{10} ln (5 x^{2} - 1) + c_{1})

Solution steps

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

Solve separable ODE:

y = ln (\frac{9}{10} ln (5 x^{2} - 1) + c_{1})

y = ln (\frac{9}{10} ln (5 x^{2} - 1) + c_{1})

\int ln (x) x^{7} d x

y = - 2 x^{4} + 7 x e^{x}

\int 3 π cos^{3} (5 π x) sin^{7} (5 π x) d x

10 t^{4}

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

What is the solution for 5x^2y^'=y^'+9xe^{-y} ?
The solution for 5x^2y^'=y^'+9xe^{-y} is y=ln(9/10 ln(5x^2-1)+c_{1})