I am reading an Abstract Algebra book, and there is a theorem that says:
Thm: If G is a finite group, then the number of elements conjugate to a is the index of the normalizer in G.
The book uses the normalizer to mean
N(a\in G)=\{ x\in G\colon xa=ax\}
Now if the group is S_4, and...
Homework Statement
Not really a homework problem, but more of a project I am working on.
Solve the following differential equation (if possible):
C=\frac{\phi ''}{\phi (\phi ' ^2 +1)^2}
Where C is a constant, and \phi is a function.
Homework Equations
See above.
The...
I don't know very much about DEQs, can someone point me in the right direction for solving this?
Note: \phi is a function of another variable and C_1, C_2 are constants.
-\phi ^2 \cdot C_1=\frac{1}{1+\phi ' ^2}+C_2
I have tried trig sub, but I didn't get anywhere.
Regards...