What is the solution for t(dy)/(dt)=t^3+12t^3y ?

The solution for t(dy)/(dt)=t^3+12t^3y is y=(e^{4t^3+c_{1}})/(12)-1/12

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t(dy)/(dt)=t^3+12t^3y

t \frac{d y}{d t} = t^{3} + 12 t^{3} y

y = \frac{e ^{4 t^{3} + c_{1}}}{12} - \frac{1}{12}

Solution steps

t \frac{d y}{d t} = t^{3} + 12 t^{3} y

Solve separable ODE:

y = \frac{e ^{4 t^{3} + c_{1}}}{12} - \frac{1}{12}

y = \frac{e ^{4 t^{3} + c_{1}}}{12} - \frac{1}{12}

\int x^{2} - x d x

x \to + 0 lim (9 x - 4)

x \to - 1 - lim (2)

\int sin^{2} (2 t) cos^{3} (2 t) d t

f (x) = x^{2} - 2, at x = 4

What is the solution for t(dy)/(dt)=t^3+12t^3y ?
The solution for t(dy)/(dt)=t^3+12t^3y is y=(e^{4t^3+c_{1}})/(12)-1/12