What is the solution for (dy)/(dt)-2ty=6t^2e^{t^2} ?

The solution for (dy)/(dt)-2ty=6t^2e^{t^2} is y=2e^{t^2}t^3+c_{1}e^{t^2}

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(dy)/(dt)-2ty=6t^2e^{t^2}

\frac{d y}{d t} - 2 t y = 6 t^{2} e^{t^{2}}

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

Solution steps

\frac{d y}{d t} - 2 t y = 6 t^{2} e^{t^{2}}

Solve linear ODE:

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

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

\frac{1}{( s ^{2} + 4 )}

\int_{- 2}^{2} (- x^{4}) - (x^{4} - 32) d x

\frac{1}{1 - x ^{2}}

f (x) = \frac{12}{x}

(4 + x) y^{^{'}} = 5 y

What is the solution for (dy)/(dt)-2ty=6t^2e^{t^2} ?
The solution for (dy)/(dt)-2ty=6t^2e^{t^2} is y=2e^{t^2}t^3+c_{1}e^{t^2}