What is the solution for (dy)/(dt)=-2ty+4e^{-t^2} ?

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

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(dy)/(dt)=-2ty+4e^{-t^2}

\frac{d y}{d t} = - 2 t y + 4 e^{- t^{2}}

y = \frac{4 t}{e ^{t^{2}}} + \frac{c _{1}}{e ^{t^{2}}}

Solution steps

\frac{d y}{d t} = - 2 t y + 4 e^{- t^{2}}

Solve linear ODE:

y = \frac{4 t}{e ^{t^{2}}} + \frac{c _{1}}{e ^{t^{2}}}

y = \frac{4 t}{e ^{t^{2}}} + \frac{c _{1}}{e ^{t^{2}}}

\frac{d}{d x} (x^{\frac{2}{3}} (\frac{5}{2} - x))

\frac{2 x + 3}{3 x - 2}

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x \to \infty lim (2 (x)^{2})

\int \frac{5}{x ^{2} - 36} d x

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