What is the solution for (dy)/(dt)-2ty=3t^2e^{t^2} ?

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

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(dy)/(dt)-2ty=3t^2e^{t^2}

\frac{d y}{d t} - 2 t y = 3 t^{2} e^{t^{2}}

y = e^{t^{2}} t^{3} + c_{1} e^{t^{2}}

Solution steps

\frac{d y}{d t} - 2 t y = 3 t^{2} e^{t^{2}}

Solve linear ODE:

y = e^{t^{2}} t^{3} + c_{1} e^{t^{2}}

y = e^{t^{2}} t^{3} + c_{1} e^{t^{2}}

\int_{0}^{π} cos^{2} (t) d t

f (x) = x^{e^{x}}

\int (x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) d x

\int \frac{14 x - 13}{x ^{2} - 4 x - 21} d x

\frac{\partial}{\partial x} (\frac{7 y}{x ^{2} + y ^{2} + 19})

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