Originally Posted by sasikanth
I have two second order differential equation which needs to be solved.
x1''(t) = 8 x2(t)
x2''(t) = 2 x1(t)

Your equations are linear with constant coefficients. I would handle either the following ways
1. Apply the Laplace transform to the equations  this will transform the problem to solving algebraic system of equations or
2. Let the solution be x
_{1}(t)=q
_{1}e
^{rt} and x
_{2}(t)=q
_{2}e
^{rt} . Substitute this assumption and you can determine r, q
_{1} and q
_{2} from eigenvalueeigenvector equation.