What is the solution for 2y^{''}-5y^'-3y=1+2e^t+e^{2t} ?

The solution for 2y^{''}-5y^'-3y=1+2e^t+e^{2t} is y=c_{1}e^{3t}+c_{2}e^{-t/2}-1/3-1/3 e^t-1/5 e^{2t}

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2y^{''}-5y^'-3y=1+2e^t+e^{2t}

2 y^{^{''}} - 5 y^{^{'}} - 3 y = 1 + 2 e^{t} + e^{2 t}

y = c_{1} e^{3 t} + c_{2} e^{- \frac{t}{2}} - \frac{1}{3} - \frac{1}{3} e^{t} - \frac{1}{5} e^{2 t}

Solution steps

2 y^{''} (t) - 5 y^{'} (t) - 3 y = 1 + 2 e^{t} + e^{2 t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- \frac{t}{2}} - \frac{1}{3} - \frac{1}{3} e^{t} - \frac{1}{5} e^{2 t}

y = c_{1} e^{3 t} + c_{2} e^{- \frac{t}{2}} - \frac{1}{3} - \frac{1}{3} e^{t} - \frac{1}{5} e^{2 t}

What is the solution for 2y^{''}-5y^'-3y=1+2e^t+e^{2t} ?
The solution for 2y^{''}-5y^'-3y=1+2e^t+e^{2t} is y=c_{1}e^{3t}+c_{2}e^{-t/2}-1/3-1/3 e^t-1/5 e^{2t}