Final answer:
The general solution to the given homogeneous differential equation is u = c1e(-0.5+0.5i)ct + c2e(-0.5-0.5i)ct, where c1 and c2 are arbitrary constants.
Step-by-step explanation:
The general solution to the given homogeneous differential equation is u = c1e(-0.5+0.5i)ct + c2e(-0.5-0.5i)ct, where c1 and c2 are arbitrary constants. This solution is obtained by using the quadratic formula to find the roots of the characteristic equation.