Page 103 - Schaum's Outline of Differential Equations

86 SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS [CHAR 9

9.8. Solve /' + 4y = 0.
The characteristic equation is

which can be factored into

These roots are a complex conjugate pair, so the general solution is given by (9.6) (with a = 0 and b = 2) as

9.9. Solve /' - 3/ + 4y = 0.
The characteristic equation is

Using the quadratic formula, we find its roots to be

These roots are a complex conjugate pair, so the general solution is given by (9.6) as

9.10. Solve y-6y + 25y = 0.
The characteristic equation is

Using the quadratic formula, we find its roots to be

These roots are a complex conjugate pair, so the general solution is

9.11. Solve

The characteristic equation is

Using the quadratic formula, we find its roots to be

These roots are a complex conjugate pair, so the general solution is

9.12. Solve /'- 8/ + I6y = 0.
The characteristic equation is

which can be factored into