What is the solution for y^{'''}+y^{''}=e^xcos(x) ?

The solution for y^{'''}+y^{''}=e^xcos(x) is y=c_{1}e^{-x}+c_{2}+c_{3}x+1/5 e^xsin(x)-1/10 e^xcos(x)

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y^{'''}+y^{''}=e^xcos(x)

y^{^{'''}} + y^{^{''}} = e^{x} cos (x)

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{1}{5} e^{x} sin (x) - \frac{1}{10} e^{x} cos (x)

Solution steps

y^{'''} (x) + y^{''} (x) = e^{x} cos (x)

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{1}{5} e^{x} sin (x) - \frac{1}{10} e^{x} cos (x)

y = c_{1} e^{- x} + c_{2} + c_{3} x + \frac{1}{5} e^{x} sin (x) - \frac{1}{10} e^{x} cos (x)

2 y^{^{''}} + 18 y = 6 tan (3 x)

y^{^{''}} + a y^{^{'}} = b

y^{^{''}} - 8 y^{^{'}} + 16 y = 10 e^{4 x} sec (x)

y^{^{''}} + 3 y^{^{'}} + 2 y = x sin (x)

y^{^{''}} + 4 y = cos^{2} (x)

What is the solution for y^{'''}+y^{''}=e^xcos(x) ?
The solution for y^{'''}+y^{''}=e^xcos(x) is y=c_{1}e^{-x}+c_{2}+c_{3}x+1/5 e^xsin(x)-1/10 e^xcos(x)