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}}

y^{^{'}} = (2 y^{2}) + x y^{2}

f^{^{'}} (x) = 2 x - \frac{3}{x ^{4}}

f (x) = \frac{2}{3 x + 1}

\int_{0}^{1} 7 e^{- 7 x} d x

x \to 5 lim (\frac{x + 2}{x - 4})

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}