What is the solution for y^{''}+2y^'+10y=3e^t+1 ?

The solution for y^{''}+2y^'+10y=3e^t+1 is y=e^{-t}(c_{1}cos(3t)+c_{2}sin(3t))+3/13 e^t+1/10

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y^{''}+2y^'+10y=3e^t+1

y^{^{''}} + 2 y^{^{'}} + 10 y = 3 e^{t} + 1

y = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{3}{13} e^{t} + \frac{1}{10}

Solution steps

y^{''} (t) + 2 y^{'} (t) + 10 y = 3 e^{t} + 1

Solve linear ODE:

y = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{3}{13} e^{t} + \frac{1}{10}

y = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{3}{13} e^{t} + \frac{1}{10}

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What is the solution for y^{''}+2y^'+10y=3e^t+1 ?
The solution for y^{''}+2y^'+10y=3e^t+1 is y=e^{-t}(c_{1}cos(3t)+c_{2}sin(3t))+3/13 e^t+1/10