What is the solution for (dy)/(dt)=t^2+13t^2y ?

The solution for (dy)/(dt)=t^2+13t^2y is y=(e^{(13t^3+c_{1})/3})/(13)-1/13

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(dy)/(dt)=t^2+13t^2y

\frac{d y}{d t} = t^{2} + 13 t^{2} y

y = \frac{e ^{\frac{13 t ^{3} + c _{1}}{3}}}{13} - \frac{1}{13}

Solution steps

\frac{d y}{d t} = t^{2} + 13 t^{2} y

Solve separable ODE:

y = \frac{e ^{\frac{13 t ^{3} + c _{1}}{3}}}{13} - \frac{1}{13}

y = \frac{e ^{\frac{13 t ^{3} + c _{1}}{3}}}{13} - \frac{1}{13}

\int (e^{x} + x cos (y)) d y

\int_{3}^{6} \frac{x}{x ^{2} + 4 x + 13} d x

\int \frac{x ^{4}}{x ^{10} - 1} d x

f (x) = \frac{7}{x - 6}

e^{k x}

What is the solution for (dy)/(dt)=t^2+13t^2y ?
The solution for (dy)/(dt)=t^2+13t^2y is y=(e^{(13t^3+c_{1})/3})/(13)-1/13