What is the solution for y^{''}+4y^'+29y=200sin(x) ?

The solution for y^{''}+4y^'+29y=200sin(x) is y=e^{-2x}(c_{1}cos(5x)+c_{2}sin(5x))+7sin(x)-cos(x)

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y^{''}+4y^'+29y=200sin(x)

y^{^{''}} + 4 y^{^{'}} + 29 y = 200 sin (x)

y = e^{- 2 x} (c_{1} cos (5 x) + c_{2} sin (5 x)) + 7 sin (x) - cos (x)

Solution steps

y^{''} (x) + 4 y^{'} (x) + 29 y = 200 sin (x)

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (5 x) + c_{2} sin (5 x)) + 7 sin (x) - cos (x)

y = e^{- 2 x} (c_{1} cos (5 x) + c_{2} sin (5 x)) + 7 sin (x) - cos (x)

\frac{d ^{2} y}{d x ^{2}} + 2 y = 6 x, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} (p) + 6 y^{^{'}} (p) + 9 y (p) = p

y^{^{''}} - 2 y^{^{'}} - 35 y = 768 e^{- t}

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12

y^{^{''}} + 4 y = sec (22 x)

What is the solution for y^{''}+4y^'+29y=200sin(x) ?
The solution for y^{''}+4y^'+29y=200sin(x) is y=e^{-2x}(c_{1}cos(5x)+c_{2}sin(5x))+7sin(x)-cos(x)