What is the solution for y^'=(ln(x))/(xy) ?

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

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y^'=(ln(x))/(xy)

y^{^{'}} = \frac{ln ( x )}{x y}

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

Solution steps

y^{'} (x) = \frac{ln ( x )}{x y}

Solve separable ODE:

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

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

\frac{d y}{d x} = - \frac{1}{sin ( y )}, y (- 3) = \frac{π}{2}

\frac{d y}{d x} (- y cot (x)) = \frac{sin ( 2 x )}{2}

y^{^{'}} = \frac{x ^{2} + 7 x + 3}{y ^{2}}, y (0) = 3

4 d y + y d x = x^{2} d y, y (4) = - 1

y^{^{'}} + (x + 2) y = 0

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