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

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

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(dy)/(dx)+(2xy)/(x^2-1)= x/(x^2-1)

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

y = - \frac{c _{1}}{2 ( x ^{2} - 1 )} + \frac{1}{2}

Solution steps

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

Solve separable ODE:

y = - \frac{c _{1}}{2 ( x ^{2} - 1 )} + \frac{1}{2}

y = - \frac{c _{1}}{2 ( x ^{2} - 1 )} + \frac{1}{2}

\frac{d y}{d x} = - \frac{8}{4} x^{3} y^{5}

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

[k \cdot f (x)] = k \cdot f^{^{'}} (x)

y^{^{'}} = \frac{1}{4} y^{2}

(t^{2} - 22 t + 96) y^{^{'}} = y

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