What is the solution for (dy)/(dt)=(3t^2)/(8y) ?

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

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(dy)/(dt)=(3t^2)/(8y)

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = (8 x - 5) (y + 2)

(e^{y} + 1)^{2} e^{- y} d x + (e^{x} + 1)^{2} e^{- x} d y = 0

(y^{2} + y) d x - (x^{2} + x) d y = 0

\frac{d y}{d x} + \frac{y}{4} = 0

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

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