What is the solution for (dy)/(dt)-2ty=-12t^2e^{t^2} ?

The solution for (dy)/(dt)-2ty=-12t^2e^{t^2} is y=-4e^{t^2}t^3+c_{1}e^{t^2}

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(dy)/(dt)-2ty=-12t^2e^{t^2}

\frac{d y}{d t} - 2 t y = - 12 t^{2} e^{t^{2}}

y = - 4 e^{t^{2}} t^{3} + c_{1} e^{t^{2}}

Solution steps

\frac{d y}{d t} - 2 t y = - 12 t^{2} e^{t^{2}}

Solve linear ODE:

y = - 4 e^{t^{2}} t^{3} + c_{1} e^{t^{2}}

y = - 4 e^{t^{2}} t^{3} + c_{1} e^{t^{2}}

\int \frac{x ^{4} - x ^{2} + 2}{x ^{2} ( x - 1 )} d x

\int \frac{I n x}{x ^{2}} d x

\frac{d}{d v} (uv)

3 6 x^{2} + 1

\frac{1}{x + 1}, 0

What is the solution for (dy)/(dt)-2ty=-12t^2e^{t^2} ?
The solution for (dy)/(dt)-2ty=-12t^2e^{t^2} is y=-4e^{t^2}t^3+c_{1}e^{t^2}