What is the solution for y^{''}+16y=-8sin(4x)+17e^x ?

The solution for y^{''}+16y=-8sin(4x)+17e^x is y=c_{1}cos(4x)+c_{2}sin(4x)+xcos(4x)+e^x

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y^{''}+16y=-8sin(4x)+17e^x

y^{^{''}} + 16 y = - 8 sin (4 x) + 17 e^{x}

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

Solution steps

y^{''} (x) + 16 y = - 8 sin (4 x) + 17 e^{x}

Solve linear ODE:

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

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

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

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

What is the solution for y^{''}+16y=-8sin(4x)+17e^x ?
The solution for y^{''}+16y=-8sin(4x)+17e^x is y=c_{1}cos(4x)+c_{2}sin(4x)+xcos(4x)+e^x