What is the solution for y^{'''}+7y^{''}-6y^'-72y=-360 ?

The solution for y^{'''}+7y^{''}-6y^'-72y=-360 is y=c_{1}e^{3t}+c_{2}e^{-4t}+c_{3}e^{-6t}+5

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y^{'''}+7y^{''}-6y^'-72y=-360

y^{^{'''}} + 7 y^{^{''}} - 6 y^{^{'}} - 72 y = - 360

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} + c_{3} e^{- 6 t} + 5

Solution steps

y^{'''} (t) + 7 y^{''} (t) - 6 y^{'} (t) - 72 y = - 360

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} + c_{3} e^{- 6 t} + 5

y = c_{1} e^{3 t} + c_{2} e^{- 4 t} + c_{3} e^{- 6 t} + 5

y^{^{''}} + 4 y^{^{'}} = 6 e^{3 t} - 3 e^{- t}

y^{^{''}} + 4 y = 2 sin (t)

y^{^{''}} - 3 y^{^{'}} - 10 y = 54 e^{7 t}, y (0) = 5

y^{^{''}} + 9 y = - 2 e^{3} t

y^{^{'''}} - 2 y^{^{''}} = 4

What is the solution for y^{'''}+7y^{''}-6y^'-72y=-360 ?
The solution for y^{'''}+7y^{''}-6y^'-72y=-360 is y=c_{1}e^{3t}+c_{2}e^{-4t}+c_{3}e^{-6t}+5