What is the solution for (dy)/(dx)+4/(x^2-1)y=0 ?

The solution for (dy)/(dx)+4/(x^2-1)y=0 is y=(e^{c_{1}}x^2+2e^{c_{1}}x+e^{c_{1}})/(x^2-2x+1)

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(dy)/(dx)+4/(x^2-1)y=0

\frac{d y}{d x} + \frac{4}{x ^{2} - 1} y = 0

y = \frac{e ^{c_{1}} x ^{2} + 2 e ^{c_{1}} x + e ^{c_{1}}}{x ^{2} - 2 x + 1}

Solution steps

\frac{d y}{d x} + \frac{4}{x ^{2} - 1} y = 0

Solve separable ODE:

y = \frac{e ^{c_{1}} x ^{2} + 2 e ^{c_{1}} x + e ^{c_{1}}}{x ^{2} - 2 x + 1}

y = \frac{e ^{c_{1}} x ^{2} + 2 e ^{c_{1}} x + e ^{c_{1}}}{x ^{2} - 2 x + 1}

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

y^{^{'}} \cdot 1 - 4 x^{2} = y

y^{^{'}} = e^{- 2 y} sin (4 x)

\frac{d y}{d t} = \frac{k}{y}

(x + 1) y = x y^{^{'}}

What is the solution for (dy)/(dx)+4/(x^2-1)y=0 ?
The solution for (dy)/(dx)+4/(x^2-1)y=0 is y=(e^{c_{1}}x^2+2e^{c_{1}}x+e^{c_{1}})/(x^2-2x+1)