Theoretical possibility?

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Is it theoretically possible to achieve a general method to solve PDEs of mth-order and nth-degree or is there a theorem which rules out any such general solution?
 

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HallsofIvy
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What do you mean by "a general method"- in terms of what kind of functions? Solving just linear equations with constant coefficients is equivalent to solving their characteristic equation, a polynomial. And it can be shown that there are polynomials that cannot be solved in terms of radicals.
 

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