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

The higher order equation y"+y=0 can be written as a unknown d/dt[y y']=[y' y"]=[y' -y]

If this is du/dt=Au, what is the 2x2 matrix A? Find its eigenvectors and eigenvalues, and compute the solution THAT STARTS FROM y(0)=2, y'(0)=0.

2. Relevant equations

y'=Ay

y(0)=y_{0}

3. The attempt at a solution

I found matrix A

[0 1

-1 0].

The eigenvalues are i and -i, and the eigenvectors

[1 -i]^T

[1 i]^T

I found the geneal solution to be:

y(t) = c_{1}e^{it}[1 i]^T+c_{2}e^{-it}[1 -i]^T

Which is equivalent,

y(t)=c_{1}[cos(t) -sin(t)]^T + c_{2}[sin(t) cos(t)]^T

I just don't know how to incorporate the initial conditions that y(0)=2 and y'(0)=0???

Any ideas???

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Complex Eigenvectors

**Physics Forums | Science Articles, Homework Help, Discussion**