What is the solution for y^'+6y=e^{-t}-6 ?

The solution for y^'+6y=e^{-t}-6 is y= 1/(5e^t)-1+(c_{1})/(e^{6t)}

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y^'+6y=e^{-t}-6

y^{^{'}} + 6 y = e^{- t} - 6

y = \frac{1}{5 e ^{t}} - 1 + \frac{c _{1}}{e ^{6 t}}

Solution steps

y^{'} (t) + 6 y = e^{- t} - 6

Solve linear ODE:

y = \frac{1}{5 e ^{t}} - 1 + \frac{c _{1}}{e ^{6 t}}

y = \frac{1}{5 e ^{t}} - 1 + \frac{c _{1}}{e ^{6 t}}

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f (x) = \frac{8}{x ^{2} + 4}

\int 3 x^{3} + 4 x^{2} - 5 x d x

x \to 0 lim (\frac{2 ( y + x ) - 2 y}{x})

\int 6 x^{2} + 4 x - 1 d x

What is the solution for y^'+6y=e^{-t}-6 ?
The solution for y^'+6y=e^{-t}-6 is y= 1/(5e^t)-1+(c_{1})/(e^{6t)}