What is the solution for (dy)/(dt)=ysin^3(t) ?

The solution for (dy)/(dt)=ysin^3(t) is y=e^{-cos(t)+(cos^3(t))/3+c_{1}}

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(dy)/(dt)=ysin^3(t)

\frac{d y}{d t} = y sin^{3} (t)

y = e^{- c o s (t) + \frac{c o s ^{3} ( t )}{3} + c_{1}}

Solution steps

\frac{d y}{d t} = y sin^{3} (t)

Solve separable ODE:

y = e^{- c o s (t) + \frac{c o s ^{3} ( t )}{3} + c_{1}}

y = e^{- c o s (t) + \frac{c o s ^{3} ( t )}{3} + c_{1}}

y^{^{'}} + y^{2} sin (t) = 3 t^{2} y^{2}

3 y y^{^{'}} = x, y (3) = 7

\frac{d y}{d x} = \frac{( 2 x + 3 )}{2 y}

3 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = - 8

3 \frac{d y}{d x} - 7 \frac{d y}{d x} + 3 y = 0

What is the solution for (dy)/(dt)=ysin^3(t) ?
The solution for (dy)/(dt)=ysin^3(t) is y=e^{-cos(t)+(cos^3(t))/3+c_{1}}