Question

Systems of first order equations can sometimes be transformed into a single equation of
higher order. Consider the system
x
1
= −2x1
+ x2, x
2
= x1
− 2x2.
(a) 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.
(b) Find the solution of the given system that also satisfies the initial conditions x1(0) = 2,
x2(0) = 3.

Answer 1

So you can start by taking \(x_1 = -2x_1 + x_2\) and solving it for \(x_2\). You can do this by moving the \(-2x_1\) to the right. Let me know when you've got this and we'll get the next step :)