What is the solution for 9x^2(dy)/(dx)=(dy)/(dx)+2xe^{-y} ?

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

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9x^2(dy)/(dx)=(dy)/(dx)+2xe^{-y}

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

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

Solution steps

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

Solve separable ODE:

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

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

t^{4}

\frac{\partial}{\partial x} (ln (\frac{x}{y} + \frac{y}{x}))

\frac{d}{d x} (ln (sin (7 x)))

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

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

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