What is the solution for (dy)/(dt)=-4y+3e^{-t} ?

The solution for (dy)/(dt)=-4y+3e^{-t} is y= 1/(e^t)+(c_{1})/(e^{4t)}

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(dy)/(dt)=-4y+3e^{-t}

\frac{d y}{d t} = - 4 y + 3 e^{- t}

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

Solution steps

\frac{d y}{d t} = - 4 y + 3 e^{- t}

Solve linear ODE:

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

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

\int 3 x^{2} + x x d x

x \to 0 lim (\frac{x ^{2} - 9 x}{x})

(3, 3), (2, - 2)

\int x cos (n) x d x

\frac{d}{d x} ((x + 3) ln (x^{2}))

What is the solution for (dy)/(dt)=-4y+3e^{-t} ?
The solution for (dy)/(dt)=-4y+3e^{-t} is y= 1/(e^t)+(c_{1})/(e^{4t)}