(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find complex number [tex]\lambda[/tex] such that e^{[tex]\lambda[/tex]t}solves

[tex]\frac{d^{2}y}{dt^{2}}[/tex] + 4[tex]\frac{dy}{dt}[/tex] + 5y = 0

Express this solution in the form e^{at}(cos(bt) + i sin(bt))

2. Relevant equations

3. The attempt at a solution

So the first part is fine, using [tex]\lambda[/tex]^{2}+ 4[tex]\lambda[/tex] + 5 = 0 to get values of [tex]\lambda[/tex] at -2[tex]\pm[/tex]i. From here, I've been taught to use:

y = Ae^{[tex]\lambda[/tex]1t}+ Be^{[tex]\lambda[/tex]2t}but this time, it doesn't help get to the required form.

Using what I've mention, I can get to A=-2 but finding B seems to be a mystery. Any help greatly appreciated!

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# Homework Help: Find a complex number from differential equations.

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