Answer to Question #5987 in Linear Algebra for Anwar Aziz

Question

Consider the differential equation y"-y'-6y=0. show that the substitutions y1=y and y2=y' lead the following system:
y1'=y2, y2'=6y1+y2.
Using the method of diagonalization, solve this system and then solve the original differential equation.

Answer 1

y2'-6y1-y2=y"-6y-y'
We can find the solution in the form:exp(a*x) => a^2-a-6=0 =>a=(1+-5)/2={3; -2}
y=C1exp(3x)+C2exp(-2x)