Using laplace functions, solve dx/dt +7*x=5*cos(2*t)

Apply the Laplace transform: (Look up in table of Laplace transforms)

Isolate and solve for L(s)

The 2nd term is too complex as is to perform inverse Transform, use partial fraction decomposition is split it up into simpler terms.

Now apply inverse Laplace Transform using Table:

where 

The answer is 9.7 cm