What is the solution for (dy}{dx}=\frac{(4sqrt(y)log_{e}(x)))/x ?

The solution for (dy}{dx}=\frac{(4sqrt(y)log_{e}(x)))/x is y=ln^4(x)+c_{1}ln^2(x)+(c_{1}^2)/4

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(dy}{dx}=\frac{(4sqrt(y)log_{e}(x)))/x

\frac{d y}{d x} = \frac{( 4 y lo g _{e} ( x ) )}{x}

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

Solution steps

\frac{d y}{d x} = \frac{( 4 y lo g _{e} ( x ) )}{x}

Solve separable ODE:

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

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

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

- 3 cos (x), at x = \frac{π}{2}

y^{^{''}} - 14 y^{^{'}} + 49 y = e^{8 x} (x^{2} - 9 x - 2)

y^{^{'}} = 1 + e^{y - x + 5}

\int (x^{2} - 4)^{2} (2 x) d x

What is the solution for (dy}{dx}=\frac{(4sqrt(y)log_{e}(x)))/x ?
The solution for (dy}{dx}=\frac{(4sqrt(y)log_{e}(x)))/x is y=ln^4(x)+c_{1}ln^2(x)+(c_{1}^2)/4