What is the solution for y^{'''}+2y^{''}-y^'-2y=5\H(t) ?

The solution for y^{'''}+2y^{''}-y^'-2y=5\H(t) is

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y^{'''}+2y^{''}-y^'-2y=5\H(t)

y^{^{'''}} + 2 y^{^{''}} - y^{^{'}} - 2 y = 5 H (t)

y = c_{1} e^{- 2 t} + c_{2} e^{- t} + c_{3} e^{t} + e^{- 2 t} \cdot \int \frac{5 H ( t )}{3 e ^{- 2 t}} d t + e^{- t} \cdot \int - \frac{5 e ^{t} H ( t )}{2} d t + e^{t} \cdot \int \frac{5 H ( t )}{6 e ^{t}} d t

Solution steps

y^{'''} (t) + 2 y^{''} (t) - y^{'} (t) - 2 y = 5 H (t)

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- t} + c_{3} e^{t} + e^{- 2 t} \cdot \int \frac{5 H ( t )}{3 e ^{- 2 t}} d t + e^{- t} \cdot \int - \frac{5 e ^{t} H ( t )}{2} d t + e^{t} \cdot \int \frac{5 H ( t )}{6 e ^{t}} d t

y = c_{1} e^{- 2 t} + c_{2} e^{- t} + c_{3} e^{t} + e^{- 2 t} \cdot \int \frac{5 H ( t )}{3 e ^{- 2 t}} d t + e^{- t} \cdot \int - \frac{5 e ^{t} H ( t )}{2} d t + e^{t} \cdot \int \frac{5 H ( t )}{6 e ^{t}} d t

What is the solution for y^{'''}+2y^{''}-y^'-2y=5\H(t) ?
The solution for y^{'''}+2y^{''}-y^'-2y=5\H(t) is