What is the solution for x^{''}+2x^'+5x=12cos(2t)+3sin(2t) ?

The solution for x^{''}+2x^'+5x=12cos(2t)+3sin(2t) is x=e^{-t}(c_{1}cos(2t)+c_{2}sin(2t))+3sin(2t)

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x^{''}+2x^'+5x=12cos(2t)+3sin(2t)

x^{^{''}} + 2 x^{^{'}} + 5 x = 12 cos (2 t) + 3 sin (2 t)

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 3 sin (2 t)

Solution steps

x^{''} (t) + 2 x^{'} (t) + 5 x = 12 cos (2 t) + 3 sin (2 t)

Solve linear ODE:

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 3 sin (2 t)

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 3 sin (2 t)

What is the solution for x^{''}+2x^'+5x=12cos(2t)+3sin(2t) ?
The solution for x^{''}+2x^'+5x=12cos(2t)+3sin(2t) is x=e^{-t}(c_{1}cos(2t)+c_{2}sin(2t))+3sin(2t)