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

The solution for 3y^{''}+5y^'+2y=t+e^t is y=c_{1}e^{-(2t)/3}+c_{2}e^{-t}+t/2-5/4+1/10 e^t

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

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

y = c_{1} e^{- \frac{2 t}{3}} + c_{2} e^{- t} + \frac{t}{2} - \frac{5}{4} + \frac{1}{10} e^{t}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- \frac{2 t}{3}} + c_{2} e^{- t} + \frac{t}{2} - \frac{5}{4} + \frac{1}{10} e^{t}

y = c_{1} e^{- \frac{2 t}{3}} + c_{2} e^{- t} + \frac{t}{2} - \frac{5}{4} + \frac{1}{10} e^{t}

3 y^{^{''}} + y^{^{'}} - 2 y = 2 cos (x)

y^{^{''}} - 8 y^{^{'}} + 16 y = 2 t e^{4 t}

y^{^{''}} + y^{^{'}} = 3 + e^{- x}

y^{^{''}} - 2 y^{^{'}} + 2 y = 2 x - 2, y (0) = 0

y^{^{''}} - 25 y = x^{2} e^{x} - x e^{5 x}

What is the solution for 3y^{''}+5y^'+2y=t+e^t ?
The solution for 3y^{''}+5y^'+2y=t+e^t is y=c_{1}e^{-(2t)/3}+c_{2}e^{-t}+t/2-5/4+1/10 e^t