What is the highest order differential equation that was successfully solved?
Solving some second or third order differential equation is difficult and sometimes impossible. Is there a limit to successfully solving a differential equation? What is the highest order diffy-q that has a solution?
- 1 decade agoFavorite Answer
The solutions of the n-th order equation y^(n)=0 are all polynomials of order at most n-1.
- mathematicianLv 71 decade ago
It is easy enough to solve the n^th order equation
for every n. THis uses standard techniques along with knowing the solutions of the polynomial x^n=1 (i.e. the roots of unity).
On the other hand, even first order equations can be difficult to solve if they are non-linear.