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

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

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

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

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

Solution steps

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

Solve exact ODE:

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

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

\frac{\partial}{\partial x} (e^{5 x yz - 9})

\frac{\partial}{\partial y} (\frac{1}{y + 2 z})

f (t) = t^{2} - t + 1

\frac{\partial}{\partial x} (\frac{y - x}{z})

\frac{d}{d x} ((x - 2) (x + 2))

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