What is the solution for y^{'''}-y^'=7sin(t) ?

The solution for y^{'''}-y^'=7sin(t) is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+7/2 cos(t)

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y^{'''}-y^'=7sin(t)

y^{^{'''}} - y^{^{'}} = 7 sin (t)

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{7}{2} cos (t)

Solution steps

y^{'''} (t) - y^{'} (t) = 7 sin (t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{7}{2} cos (t)

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{7}{2} cos (t)

(D^{4} + D^{2}) y = 18 x - 4 sin (x)

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

y^{^{'''}} + 9 y^{^{''}} - 108 y = e^{- 6 x}

y^{^{''''}} + 2 y^{^{''}} + y = 3 t + 4

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 x} sin (2 x)

What is the solution for y^{'''}-y^'=7sin(t) ?
The solution for y^{'''}-y^'=7sin(t) is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+7/2 cos(t)