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

So my friend asked me for help because he assumed having a math degree meant I knew math

[PLAIN]http://courses.webwork.maa.org:8080/wwtmp/equations/0e/c5a05957810916cfdff379ee0642fc1.png [Broken]

(dx/dt=−4y and dy/dt = −4x)

Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for x from the first equation.

Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0) = 4 and y(0) = 1, what are x and y?

2. Relevant equations

y(t)=C1e^(at)cos(Bt) + C2e^(at)sin(Bt)

3. The attempt at a solution

So I've tried a few approaches but I've failed. This is the approach I got the farthest with.

d^2y/d^2t = -4

you can then say r^2 + 4 = 0

b^2-4ac = 0 - 4*4 = -16

r = 0 +/- sqrt(-16) / 2 = +/- 2i

y = Ae^(0t)cos(2t) + Be^(0t)sin(2t)

y=Acos(2t)+Bsin(2t)

y' =2Bcos(2t) + 2Asin(2t)

If I solve for x(t) I end up with the same equation as y(t).

If you set up for x(0)=4 and y(0)=1, you end up with:

1=A

4=A?

I know this is easy but I'm just not seeing it. Any help would be appreciated. Thanks

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# Homework Help: System of Differential Equations

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