What is the solution for (dy)/(dx)=((2yln(y)))/((x)),y(1)=4 ?

The solution for (dy)/(dx)=((2yln(y)))/((x)),y(1)=4 is y=4^{x^2}

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(dy)/(dx)=((2yln(y)))/((x)),y(1)=4

\frac{d y}{d x} = \frac{( 2 y ln ( y ) )}{( x )}, y (1) = 4

y = 4^{x^{2}}

Solution steps

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

Solve separable ODE:

y = 4^{x^{2}}

y = 4^{x^{2}}

y \frac{d y}{d x} - x y^{2} + x = 0

y^{^{'}} - 6 x y = 0, y (1) = 1

- x y + (1 - x^{2}) (\frac{d y}{d x}) = 7 x y^{2}

y^{^{'}} = \frac{e ^{5 x}}{cos ( 2 y )}

\frac{d y}{d x} = x^{2} e^{(y - x)}

What is the solution for (dy)/(dx)=((2yln(y)))/((x)),y(1)=4 ?
The solution for (dy)/(dx)=((2yln(y)))/((x)),y(1)=4 is y=4^{x^2}