What is the solution for (dy)/(dx)= x/(2sqrt(y)) ?

The solution for (dy)/(dx)= x/(2sqrt(y)) is y=(\sqrt[3]{9x^4+72c_{1}x^2+144c_{1}^2})/4

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(dy)/(dx)= x/(2sqrt(y))

\frac{d y}{d x} = \frac{x}{2 y}

y = \frac{3 9 x ^{4} + 72 c _{1} x ^{2} + 144 c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = \frac{x}{2 y}

Solve separable ODE:

y = \frac{3 9 x ^{4} + 72 c _{1} x ^{2} + 144 c _{1}^{2}}{4}

y = \frac{3 9 x ^{4} + 72 c _{1} x ^{2} + 144 c _{1}^{2}}{4}

\frac{d q}{d t} = 4 q^{2} ln (t)

y^{^{'}} + t \cdot y = y, y (1) = 3

y^{^{'}} = 2 y + 3, y (0) = 5

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

\frac{d y}{d t} = \frac{sin ^{2} ( t ) + t}{y}

What is the solution for (dy)/(dx)= x/(2sqrt(y)) ?
The solution for (dy)/(dx)= x/(2sqrt(y)) is y=(\sqrt[3]{9x^4+72c_{1}x^2+144c_{1}^2})/4