What is the solution for 9x^2(dy)/(dx)=(dy)/(dx)+5xe^{-y} ?

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

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9x^2(dy)/(dx)=(dy)/(dx)+5xe^{-y}

9 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 5 x e^{- y}

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

Solution steps

9 x^{2} \frac{d y}{d x} = \frac{d y}{d 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}{d x} ((x - 3)^{\frac{4}{5}} (x + 1)^{\frac{1}{5}})

y = 2 x^{- 3}

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

x \to 4 - lim (\frac{x - 10}{x - 4})

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