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}

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}