What is the solution for (dy)/(dt)-2ty=-12t^2e^{t^2},y(0)=-1 ?

The solution for (dy)/(dt)-2ty=-12t^2e^{t^2},y(0)=-1 is y=-4e^{t^2}t^3-e^{t^2}

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(dy)/(dt)-2ty=-12t^2e^{t^2},y(0)=-1

\frac{d y}{d t} - 2 t y = - 12 t^{2} e^{t^{2}}, y (0) = - 1

y = - 4 e^{t^{2}} t^{3} - 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} - e^{t^{2}}

y = - 4 e^{t^{2}} t^{3} - e^{t^{2}}

What is the solution for (dy)/(dt)-2ty=-12t^2e^{t^2},y(0)=-1 ?
The solution for (dy)/(dt)-2ty=-12t^2e^{t^2},y(0)=-1 is y=-4e^{t^2}t^3-e^{t^2}