# Confused on why i'm missing this 2nd Order Diff EQ with complex roots!

1. Feb 8, 2006

### mr_coffee

Hello everyone. I"m not getting this problem right. <insert sad face here>
Find y as a function of t if
6y'' + 33y = 0,
y(0) = 8, y'(0) = 5 .
y(t) =

hokay, here is my work, it is sloppy sorry. Can you see any obvious mistakes I made? Note: the sqraure root should be encompassing both the 11 and the 2 in 11/2.

http://img136.imageshack.us/img136/681/lastscan8wk.jpg [Broken]

I submitted this and it was wrong:>
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/90/5f593c3fcc529485c44d6db5c6c1ea1.png [Broken]

Last edited by a moderator: May 2, 2017
2. Feb 8, 2006

### benorin

For your general solution, that is

$$y=Ae^{i\sqrt{\frac{11}{2}}t}+Be^{-i\sqrt{\frac{11}{2}}t}$$

$$y=c_1\sin {\sqrt{\frac{11}{2}}t}+c_2\cos {\sqrt{\frac{11}{2}}t}$$

3. Feb 8, 2006

### benorin

that comes from Euler's formula $$e^{i\alpha}=\cos\alpha+i\sin\alpha$$, substituted into the general solution with the e's, some constant renaming and some trickery to show that if the new solution (with the cos + isin stuff) is a complex solution to the DE, then the same thing without the i is also a solution. But that was mostly hand-waving.

4. Feb 9, 2006

### mr_coffee

Thanks for the help again benorin, but I submitted:
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/32/eb2319e057d3fc3b2523e3d817a55a1.png [Broken]
Did i mess up finding my constants?

Last edited by a moderator: May 2, 2017