What is the solution for t(dy)/(dt)=t^3+15t^3y ?

The solution for t(dy)/(dt)=t^3+15t^3y is y=(e^{5t^3+c_{1}})/(15)-1/15

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t(dy)/(dt)=t^3+15t^3y

t \frac{d y}{d t} = t^{3} + 15 t^{3} y

y = \frac{e ^{5 t^{3} + c_{1}}}{15} - \frac{1}{15}

Solution steps

t \frac{d y}{d t} = t^{3} + 15 t^{3} y

Solve separable ODE:

y = \frac{e ^{5 t^{3} + c_{1}}}{15} - \frac{1}{15}

y = \frac{e ^{5 t^{3} + c_{1}}}{15} - \frac{1}{15}

- 6 y^{^{'}} + 18 x^{2} = 0

(t^{3}) d x + (x t^{2} + x^{3}) d t = 0

\int cos (x) - cos^{3} (x) d x

\frac{d}{d x} (- 4 x^{- 3})

What is the solution for t(dy)/(dt)=t^3+15t^3y ?
The solution for t(dy)/(dt)=t^3+15t^3y is y=(e^{5t^3+c_{1}})/(15)-1/15