Although the real general solution form (9) is convenient,

QUESTION:

Although the real general solution form (9) is convenient, it is also possible to use the form
                                

(21)          \(d_{1} e^{(\alpha+i \beta) t}\)

to solve initial value problems, as illustrated in Example 1. The coefficients \(d_{1}\) and \(d_{2}\) are complex constants.
(a) Use the form (21) to solve Problem 21. Verify that your form is equivalent to the one derived using (9).

(b) Show that, in general, \(d_{1}\) and \(d_{2}\) in (21) must be complex conjugates in order that the solution be real.

Equation Transcription:

Text Transcription:

\begin{aligned}

d_{1} e^{(alpha+i beta) t}

d_{1}

d_{2}

d_{1}

d_{2}