What is the solution for y^{'''}+9y^{''}+y^'+9y=16e^x-9 ?

The solution for y^{'''}+9y^{''}+y^'+9y=16e^x-9 is y=c_{1}e^{-9x}+c_{2}cos(x)+c_{3}sin(x)+4/5 e^x-1

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y^{'''}+9y^{''}+y^'+9y=16e^x-9

y^{^{'''}} + 9 y^{^{''}} + y^{^{'}} + 9 y = 16 e^{x} - 9

y = c_{1} e^{- 9 x} + c_{2} cos (x) + c_{3} sin (x) + \frac{4}{5} e^{x} - 1

Solution steps

y^{'''} (x) + 9 y^{''} (x) + y^{'} (x) + 9 y = 16 e^{x} - 9

Solve linear ODE:

y = c_{1} e^{- 9 x} + c_{2} cos (x) + c_{3} sin (x) + \frac{4}{5} e^{x} - 1

y = c_{1} e^{- 9 x} + c_{2} cos (x) + c_{3} sin (x) + \frac{4}{5} e^{x} - 1

What is the solution for y^{'''}+9y^{''}+y^'+9y=16e^x-9 ?
The solution for y^{'''}+9y^{''}+y^'+9y=16e^x-9 is y=c_{1}e^{-9x}+c_{2}cos(x)+c_{3}sin(x)+4/5 e^x-1