Discuss: How can the procedure in Exercise 7 be used to solve y‴ - 6y″ + 11y′ - 6y = 0? Carry out your ideas.
Exercise 7
It is possible to solve a single differential equation by expressing the equation as a system and then using the method of this section. For the differential equation y′′ - y′ - 6y = 0, show that the substitutions y1 = y and y2 = y′ lead to the system
y′1 = y2
y′2 = 6y1 + y2
Solve this system and then solve the original differential equation.