What is the solution for (dy)/(dx)=(sqrt(x^3))/(2y),y(0)=-4 ?

The solution for (dy)/(dx)=(sqrt(x^3))/(2y),y(0)=-4 is y=-sqrt((2x^{5/2))/5+16}

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(dy)/(dx)=(sqrt(x^3))/(2y),y(0)=-4

\frac{d y}{d x} = \frac{x ^{3}}{2 y}, y (0) = - 4

y = - \frac{2 x ^{\frac{5}{2}}}{5} + 16

Solution steps

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

Solve separable ODE:

y = - \frac{2 x ^{\frac{5}{2}}}{5} + 16

y = - \frac{2 x ^{\frac{5}{2}}}{5} + 16

y^{^{'}} + y = - 2

x \frac{d y}{d x} = e^{10 y + x}, x > 0

y^{^{'}} + y = 10

y^{^{'}} = 1 - y^{2}, y (0) = 0

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

What is the solution for (dy)/(dx)=(sqrt(x^3))/(2y),y(0)=-4 ?
The solution for (dy)/(dx)=(sqrt(x^3))/(2y),y(0)=-4 is y=-sqrt((2x^{5/2))/5+16}