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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d}{d x} (\frac{x ^{4} - 5 x ^{3} + x}{x ^{2}})

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

x \to - \infty lim (4 x)

\int \frac{1}{3 - 2 x} d x

\int \frac{1}{1 + 4 x ^{2}} d x

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