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# 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?

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- 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

y^(n)=y

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.

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