What is the solution for y^'+6y=t+e^{-5t} ?

The solution for y^'+6y=t+e^{-5t} is y=(6t-1)/(36)+1/(e^{5t)}+(c_{1})/(e^{6t)}

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y^'+6y=t+e^{-5t}

y^{^{'}} + 6 y = t + e^{- 5 t}

y = \frac{6 t - 1}{36} + \frac{1}{e ^{5 t}} + \frac{c _{1}}{e ^{6 t}}

Solution steps

y^{'} (t) + 6 y = t + e^{- 5 t}

Solve linear ODE:

y = \frac{6 t - 1}{36} + \frac{1}{e ^{5 t}} + \frac{c _{1}}{e ^{6 t}}

y = \frac{6 t - 1}{36} + \frac{1}{e ^{5 t}} + \frac{c _{1}}{e ^{6 t}}

What is the solution for y^'+6y=t+e^{-5t} ?
The solution for y^'+6y=t+e^{-5t} is y=(6t-1)/(36)+1/(e^{5t)}+(c_{1})/(e^{6t)}