What is the solution for (dy)/(dt)=(9t^2)/(8y) ?

The solution for (dy)/(dt)=(9t^2)/(8y) is y=(sqrt(c_{1)+3t^3})/2 ,y=-(sqrt(c_{1)+3t^3})/2

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(dy)/(dt)=(9t^2)/(8y)

\frac{d y}{d t} = \frac{9 t ^{2}}{8 y}

y = \frac{c _{1} + 3 t ^{3}}{2}, y = - \frac{c _{1} + 3 t ^{3}}{2}

Solution steps

\frac{d y}{d t} = \frac{9 t ^{2}}{8 y}

Solve separable ODE:

y = \frac{c _{1} + 3 t ^{3}}{2}, y = - \frac{c _{1} + 3 t ^{3}}{2}

y = \frac{c _{1} + 3 t ^{3}}{2}, y = - \frac{c _{1} + 3 t ^{3}}{2}

cos (y) d y = sin (x) d x

\frac{d y}{d x} = \frac{4 x}{3 y + 1}

x \frac{d y}{d x} - (1 - x^{2}) y = 0

y^{^{'}} = x y^{\frac{1}{2}}, y (0) = \frac{1}{16} x^{4}

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

What is the solution for (dy)/(dt)=(9t^2)/(8y) ?
The solution for (dy)/(dt)=(9t^2)/(8y) is y=(sqrt(c_{1)+3t^3})/2 ,y=-(sqrt(c_{1)+3t^3})/2