What is the solution for (dy)/(dx)=(sqrt(x^3))/(2y) ?

The solution for (dy)/(dx)=(sqrt(x^3))/(2y) is y=sqrt(2/5 x^{5/2)+c_{1}},y=-sqrt(2/5 x^{5/2)+c_{1}}

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(dy)/(dx)=(sqrt(x^3))/(2y)

\frac{d y}{d x} = \frac{x ^{3}}{2 y}

y = \frac{2}{5} x^{\frac{5}{2}} + c_{1}, y = - \frac{2}{5} x^{\frac{5}{2}} + c_{1}

Solution steps

\frac{d y}{d x} = \frac{x ^{3}}{2 y}

Solve separable ODE:

y = \frac{2}{5} x^{\frac{5}{2}} + c_{1}, y = - \frac{2}{5} x^{\frac{5}{2}} + c_{1}

y = \frac{2}{5} x^{\frac{5}{2}} + c_{1}, y = - \frac{2}{5} x^{\frac{5}{2}} + c_{1}

x y^{^{'}} = (x + 1) y

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

3 y^{2} \frac{d y}{d x} = 8 x

y^{^{'}} = 15 y - y^{2} - 50

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

What is the solution for (dy)/(dx)=(sqrt(x^3))/(2y) ?
The solution for (dy)/(dx)=(sqrt(x^3))/(2y) is y=sqrt(2/5 x^{5/2)+c_{1}},y=-sqrt(2/5 x^{5/2)+c_{1}}