What is the solution for x^{''}+x=8cos(5t) ?

The solution for x^{''}+x=8cos(5t) is x=c_{1}cos(t)+c_{2}sin(t)-1/3 cos(5t)

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x^{''}+x=8cos(5t)

x^{^{''}} + x = 8 cos (5 t)

x = c_{1} cos (t) + c_{2} sin (t) - \frac{1}{3} cos (5 t)

Solution steps

x^{''} (t) + x = 8 cos (5 t)

Solve linear ODE:

x = c_{1} cos (t) + c_{2} sin (t) - \frac{1}{3} cos (5 t)

x = c_{1} cos (t) + c_{2} sin (t) - \frac{1}{3} cos (5 t)

What is the solution for x^{''}+x=8cos(5t) ?
The solution for x^{''}+x=8cos(5t) is x=c_{1}cos(t)+c_{2}sin(t)-1/3 cos(5t)