# Fundamentals of Differential Equations

Section 4.3 (p. 186)- Auxiliary Equations with Complex
Roots

5. Find a general solution to the DE

The general solution is

17. Find a general solution to the equation

The general solution is

23. Solve the initial value problem

The general solution is .

Since

The specific solution is

29 Find a general solution to the DE

is a solution.

Using synthetic division we get

The general solution is

The possible integer solutions are

± 1, 2, 13, and 26 .

Try graph
and you will

see that is a zero of the function

The general solution is

The general solution is