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

The solution for y^{''}-2y^'+y=3sqrt(t+1)e^{-t} is

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

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

y = c_{1} e^{t} + c_{2} t e^{t} + e^{t} \cdot \int - \frac{3 t t + 1}{e ^{2 t}} d t + \frac{3 2 e ^{2}}{2} e^{t} t (- \frac{1}{2} e^{- 2 t - 2} 2 t + 2 + \frac{π}{4} erf (2 t + 2))

Solution steps

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} + e^{t} \cdot \int - \frac{3 t t + 1}{e ^{2 t}} d t + \frac{3 2 e ^{2}}{2} e^{t} t (- \frac{1}{2} e^{- 2 t - 2} 2 t + 2 + \frac{π}{4} erf (2 t + 2))

y = c_{1} e^{t} + c_{2} t e^{t} + e^{t} \cdot \int - \frac{3 t t + 1}{e ^{2 t}} d t + \frac{3 2 e ^{2}}{2} e^{t} t (- \frac{1}{2} e^{- 2 t - 2} 2 t + 2 + \frac{π}{4} erf (2 t + 2))

What is the solution for y^{''}-2y^'+y=3sqrt(t+1)e^{-t} ?
The solution for y^{''}-2y^'+y=3sqrt(t+1)e^{-t} is