What is the solution for (dy)/(dt)=-4y+9e^{-t} ?

The solution for (dy)/(dt)=-4y+9e^{-t} is y= 3/(e^t)+(c_{1})/(e^{4t)}

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(dy)/(dt)=-4y+9e^{-t}

\frac{d y}{d t} = - 4 y + 9 e^{- t}

y = \frac{3}{e ^{t}} + \frac{c _{1}}{e ^{4 t}}

Solution steps

\frac{d y}{d t} = - 4 y + 9 e^{- t}

Solve linear ODE:

y = \frac{3}{e ^{t}} + \frac{c _{1}}{e ^{4 t}}

y = \frac{3}{e ^{t}} + \frac{c _{1}}{e ^{4 t}}

\int 4 sin^{3} (x) cos^{2} (x) d x

x \to 0 + lim ((1 + x)^{\frac{4}{x}})

\int \frac{x ^{2}}{5 - 4 x ^{2}} d x

x \to - \infty lim (\frac{1}{9} arctan (x))

\frac{d}{d x} (ln (3 x))

What is the solution for (dy)/(dt)=-4y+9e^{-t} ?
The solution for (dy)/(dt)=-4y+9e^{-t} is y= 3/(e^t)+(c_{1})/(e^{4t)}