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

The solution for (dy)/(dx)-2/x y-1/(xy)=0 is y=sqrt((c_{1)x^4-1)/2},y=-sqrt((c_{1)x^4-1)/2}

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

\frac{d y}{d x} - \frac{2}{x} y - \frac{1}{x y} = 0

y = \frac{c _{1} x ^{4} - 1}{2}, y = - \frac{c _{1} x ^{4} - 1}{2}

Solution steps

\frac{d y}{d x} - \frac{2}{x} y - \frac{1}{x y} = 0

Solve separable ODE:

y = \frac{c _{1} x ^{4} - 1}{2}, y = - \frac{c _{1} x ^{4} - 1}{2}

y = \frac{c _{1} x ^{4} - 1}{2}, y = - \frac{c _{1} x ^{4} - 1}{2}

\frac{d y}{d t} = 0.1 y, y (0) = 600, t = 5

sin (3 x) d x + 4 y cos^{2} (3 x) d y = 0

\frac{d y}{d x} = \frac{2 x}{- 8 y - 6}, y (0) = - 8

(1 + x^{2}) y^{^{'}} + 2 x y = - x

y^{^{'}} = - 2 t y

What is the solution for (dy)/(dx)-2/x y-1/(xy)=0 ?
The solution for (dy)/(dx)-2/x y-1/(xy)=0 is y=sqrt((c_{1)x^4-1)/2},y=-sqrt((c_{1)x^4-1)/2}