Confused on how my professor did this last step, DiffEQ, 2nd OrdER

mr_coffee
Messages
1,613
Reaction score
1
Hello everyone!
My professor was going over a problem real fast for the exam and now that i went over it again, I'm lost on how he did this last step. He is using a method called Abels Theorum. THe problem says:
Find a second solution of the given differential equation:
t^2y''+3ty' + y = 0;
y1(t) = 1/t;

U could use Eulers, but he doesn't want us to use that method, you could also use reduction of order but that would be more work and he doesn't want us to use that method either. He wants us to use Abels therom which seems to be the simplest out of all of them. Here is my work and I noted where I was confused at the very bottom of the page:


http://suprfile.com/src/1/2bgbtx/lastscan.jpg

Thanks if your confused on my work, let me know and i'll explain!
 
Last edited by a moderator:
Physics news on Phys.org
Are you sure that the line shouldn't be ty_2=ln|t|+C
 
oooo,
w00t
yeah ur right! the t magically dissapears then reappears!
thanks again assyrian!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top