What is the solution for y^{''}+2y^'+17y=-44-85x ?

The solution for y^{''}+2y^'+17y=-44-85x is y=e^{-x}(c_{1}cos(4x)+c_{2}sin(4x))-5x-2

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y^{''}+2y^'+17y=-44-85x

y^{^{''}} + 2 y^{^{'}} + 17 y = - 44 - 85 x

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

Solution steps

y^{''} (x) + 2 y^{'} (x) + 17 y = - 44 - 85 x

Solve linear ODE:

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

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

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 e^{3 x} + 2 sin (x) - cos (x)

2 y^{^{''}} + 2 y = - 16 cos (3 x)

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

y^{^{''}} - 3 y^{^{'}} - 4 y = e^{2 x}

What is the solution for y^{''}+2y^'+17y=-44-85x ?
The solution for y^{''}+2y^'+17y=-44-85x is y=e^{-x}(c_{1}cos(4x)+c_{2}sin(4x))-5x-2