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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\int - 2 x 8 - x^{2} d x

x \to 0 + lim (\frac{x - ∣ x ∣}{x})

e^{x + 1}

- y^{^{'}} + \frac{2 y}{x} = \frac{y ^{2}}{x}

x \to \infty lim (ln (3 x) - ln (x + 7))

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