What is the solution for (dy)/(dt)-2ty=15t^2e^{t^2} ?

The solution for (dy)/(dt)-2ty=15t^2e^{t^2} is y=5e^{t^2}t^3+c_{1}e^{t^2}

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(dy)/(dt)-2ty=15t^2e^{t^2}

\frac{d y}{d t} - 2 t y = 15 t^{2} e^{t^{2}}

y = 5 e^{t^{2}} t^{3} + c_{1} e^{t^{2}}

Solution steps

\frac{d y}{d t} - 2 t y = 15 t^{2} e^{t^{2}}

Solve linear ODE:

y = 5 e^{t^{2}} t^{3} + c_{1} e^{t^{2}}

y = 5 e^{t^{2}} t^{3} + c_{1} e^{t^{2}}

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What is the solution for (dy)/(dt)-2ty=15t^2e^{t^2} ?
The solution for (dy)/(dt)-2ty=15t^2e^{t^2} is y=5e^{t^2}t^3+c_{1}e^{t^2}