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

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

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

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

y = c_{1} x^{2} - 1

Solution steps

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

Solve separable ODE:

y = c_{1} x^{2} - 1

y = c_{1} x^{2} - 1

x^{^{'}} = \frac{1}{2} (x^{2} - 1)

\frac{d t}{d x} = 3 x t^{2}

\frac{d x}{d t} = - 0.6364 x

y^{^{'}} tan (x) = y ln (y)

\frac{d y}{d t} = \frac{[ 3 t ^{2} + 4 t + 2 ]}{[ 2 y - 2 ]}, y (0) = - 1

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