I'm not a math genius. Do I have a shot?

[Will James]

I suppose DE == ODE?
For nonlinear DEs, it is possible to have no solutions, multiple solutions etc.

A solution may not exist in the classical sense and then we need weak solutions.

And how can we 'compute' the solution?

Those you mentioned are in the discussion on existence & uniqueness as well.

When it comes to existence, sometimes there is no solution.

When it comes to uniqueness, sometimes there are multiple solutions, not just one solution.

Some explicit solutions are at best difficult to obtain and at worst impossible to obtain.
That's why mathematicians study DE.

In brief, there are different approaches to the study of DEs
1) Analytical approach
2) Quantitative analysis
3) Numerical analysis

If a DE cannot be solved by analytical methods, yet we can prove that a solution exists, the next logical query is, Can we somehow approximate the values of an unknown solution?
THE ANSWER to this question is numerical analysis.

 

[ExSan]

I'm not a math genius. Do I have a shot?
no, you don't

 

[Connor Whelan]

If you want to work at some of the best quant hedge funds then yeah you probably have to be somewhat of a math genius. You should be able to get your foot in the door at a bank if you work hard to learn everything on the quant reading list and practice brain teasers. Getting a masters in stats, applied math, FE, or OR would definitely increase your odds.