What is the solution for ln(x)y^'-(2sqrt(y))/x =0 ?

The solution for ln(x)y^'-(2sqrt(y))/x =0 is y=ln^2(ln(x))+c_{1}ln(ln(x))+(c_{1}^2)/4

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ln(x)y^'-(2sqrt(y))/x =0

ln (x) y^{^{'}} - \frac{2 y}{x} = 0

y = ln^{2} (ln (x)) + c_{1} ln (ln (x)) + \frac{c _{1}^{2}}{4}

Solution steps

ln (x) y^{'} (x) - \frac{2 y}{x} = 0

Solve separable ODE:

y = ln^{2} (ln (x)) + c_{1} ln (ln (x)) + \frac{c _{1}^{2}}{4}

y = ln^{2} (ln (x)) + c_{1} ln (ln (x)) + \frac{c _{1}^{2}}{4}

3 e^{7 x} \frac{d y}{d x} = - 49 \frac{x}{y ^{2}}, y (0) = 1

a y d x + x d y = 0

y^{^{'}} 2 y = 3 e^{4 x} - 4 sin (4 x), y (0) = - 5

3 y \cdot d x - x \cdot d y = 0

y^{^{'}} (t) = \frac{t}{( 1 + y ^{2} )}, y (0) = 0

What is the solution for ln(x)y^'-(2sqrt(y))/x =0 ?
The solution for ln(x)y^'-(2sqrt(y))/x =0 is y=ln^2(ln(x))+c_{1}ln(ln(x))+(c_{1}^2)/4