1. Consider the homogeneous differential equation
2y" - 6y" - 2y + 6y = 0.
1. Verify that ex, ex, and ex
2. Prove that the Span([ex, ex, e³x]) is a vector space.
are solutions of the differential equation.

1 Consider the homogeneous differential equation 2y 6y 2y 6y 0 1 Verify that ex ex and ex 2 Prove that the Spanex ex ex is a vector space are solutions of the d class=