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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} + 12 x^{2} y = 5 x^{2}, y (0) = 4

y^{^{'}} - 2 x y - x = 0

x \frac{d y}{d x} = e^{4 y + x}

y^{^{'}} = y^{2} x cos (x^{2})

\frac{d y}{d x} = x \cdot e^{y}

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