What is the solution for (dy}{dx}=\frac{sqrt(y)ln(x))/x ,y(1)=0 ?

The solution for (dy}{dx}=\frac{sqrt(y)ln(x))/x ,y(1)=0 is y=(ln^4(x))/(16)

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(dy}{dx}=\frac{sqrt(y)ln(x))/x ,y(1)=0

\frac{d y}{d x} = \frac{y ln ( x )}{x}, y (1) = 0

y = \frac{ln ^{4} ( x )}{16}

Solution steps

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

Solve separable ODE:

y = \frac{ln ^{4} ( x )}{16}

y = \frac{ln ^{4} ( x )}{16}

(1 - x) y^{^{'}} - y = 0

d v = sin (x) d x

\frac{d x}{d t} = 1 - x

2 x y^{3} d x + 3 x^{2} y^{2} d y = 0, y (1) = 2

5 x \frac{d y}{d x} = 6 (7 - 3 y)

What is the solution for (dy}{dx}=\frac{sqrt(y)ln(x))/x ,y(1)=0 ?
The solution for (dy}{dx}=\frac{sqrt(y)ln(x))/x ,y(1)=0 is y=(ln^4(x))/(16)