What is the solution for (dy)/(dx)=(2ln(x))/(xy) ?

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

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(dy)/(dx)=(2ln(x))/(xy)

\frac{d y}{d x} = \frac{2 ln ( x )}{x y}

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

Solution steps

\frac{d y}{d x} = \frac{2 ln ( x )}{x y}

Solve separable ODE:

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

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

\frac{d y}{d x} + x^{4} y = 4 x^{4}

x^{^{'}} = \frac{x ^{2} + x}{2 x + 1}, x (0) = 1

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

y - x y^{^{'}} = 1992 (1 + x^{2} y^{^{'}})

sin (x) \frac{d y}{d x} + cos (x) y = 0

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