What is the solution for x^{''}+4x=10cos(3t) ?

The solution for x^{''}+4x=10cos(3t) is x=c_{1}cos(2t)+c_{2}sin(2t)-2cos(3t)

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x^{''}+4x=10cos(3t)

x^{^{''}} + 4 x = 10 cos (3 t)

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

Solution steps

x^{''} (t) + 4 x = 10 cos (3 t)

Solve linear ODE:

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

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

What is the solution for x^{''}+4x=10cos(3t) ?
The solution for x^{''}+4x=10cos(3t) is x=c_{1}cos(2t)+c_{2}sin(2t)-2cos(3t)