Systems of first order equations can sometimes be transformed into a single equation of
higher order. Consider the system
(1) x1' = -2x1 + x2
(2) x2' = x1 - 2x2
Solve the first equation for x2 and substitute into the second equation, thereby obtaining a second order equation for x1. Solve this equation for x1 and then determine x2 also.
The Attempt at a Solution
Solving (1) for x2 yields:
x2 = x1' + 2x1
Substituting into (2) yields:
x2' = x1 - 2(x1' + 2x1)
x2' = -3x1 - 2x1'
How am I supposed to solve this now with the x2' term there?