Is There a Universal Method to Solve All Types of PDEs?

[sid_galt]

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?

 

[HallsofIvy]

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.