What is the solution for (dy)/(dx)=((9x)/(9x^2-1))e^{-y} ?

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

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(dy)/(dx)=((9x)/(9x^2-1))e^{-y}

\frac{d y}{d x} = (\frac{9 x}{9 x ^{2} - 1}) e^{- y}

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

Solution steps

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

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

x^{4} - 3 x^{2} + 1, 1

y = e^{x} (x + x x)

x \to - 2 lim (4 x^{2} - 3)

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