question: Use complex exponentials to find the solution of the differential equation(adsbygoogle = window.adsbygoogle || []).push({});

(d^2y(t)/dt^2) + (3dy(t)/dt) + (25/4)y(t) = 0

such that y(0) = 0, dy/dt =1 for t=o

my taughts: I started by putting it in the form m^2 + 3m +25/4

m = (-3sqrt(9-25))/2 = (-3sqrt(-16))/2 = (-3+-4i)/2

then i thaught one can put it in the form e^pt(AcosQt+BsinQt) [p+-Qi]

so: y = (e^(-3/2)t)(Acos2t + Bsin2t)

y(0)=0 dy/dt=1 for t=0 y=Ae^(((-3+4i)/2)t) + Be^(((-3-4i)/2)t)

0 = (e^(-3/2)t)(Acos2t + Bsin2t)

0 = (Acos2t + Bsin2t)

0 = A + 0

A=0

dy/dt = (-3/2(e^(-3/2)t))(Acos2theta + Bsin2theta) + (e^(-3/2)t)(-2Asin2t + 2Bcos2t)

1=(-3/2)A +2B

2B = 1 (because A=0)

B=1/2

so y(t) = e^((-3/2)t) ((1/2)sin2t)

Don't know if I have done the question right or even got the question at all. just wanted to know if this is right, or if i'm on the right track but made a misstake on the way. Also if I'm completly wrong please point that out and give me a pointer where to start.

edit: sorry for posting this in both precalc and in calc, just didn't know where it belongs....i'm swedish don't actually know the definition for calculus.

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# Complex exponentials and differential equations

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