# Differential equations

Hi,

Please help solving these problems

section 4.3 # 4,16,22,34,38

See attached

The auxiliary equation for the given differential equation has complex roots. Find a general solution.

Solve the given initial value problem.

Prove the sum of angle formula for the sine function by following these steps.

https://brainmass.com/math/calculus-and-analysis/differential-equations-examples-initial-value-problem-208591

#### Solution Preview

Please see the attached file for detailed solution.

4. if the auxiliary equation has complex roots , the general solution has the form of , where C1 and C2 are both constants

The auxiliary equation is

The roots are:

Then the general solution is

16. The auxiliary equation is

The roots are:

Since the auxiliary equation has two district real roots, the general solution ...

#### Solution Summary

This provides several examples of working with differential equations, including initial value problem, complex roots, a proof of the sum of angle formula, and an RLC series circuit.