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

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

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(x^2y-x)dy+ydx=0

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

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

Solution steps

(x^{2} y - x) d y + y d x = 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{d}{d x} (\frac{10}{x ^{7}})

y = 9 x, y = \frac{1}{3} x, y = 10 - x^{2}

tan (x y)

1 - 8 u^{2}

\int_{0}^{1} 2 π x (e^{- x^{2}}) d x

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