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Question: Solving a system of equations that has a PDE

Question:Solving a system of equations that has a PDE

rt54321 10 Maple
pde differential-equations
December 04 2022
1

I have seen several examples of using Maple to numerically solve a PDE, but I'm looking for a "symbolic" method.

Very basic exampl - I have a system of differential equations with two state variables [x1 and x2] like so:
 
x1_prime = x2 + u*x1 + dH/dx1      <--- dH/dx1 is the partial deriv of H wrt x1
x2_prime = x1 + dH/dx2                 <--- dH/dx2 is the partial deriv of H wrt x2
 
H is the energy function that I'm trying to find.
--> I know the partial derivatives of the function H (from above), but I don't know what H itself is. Is there a Maple function or example that will help me find H symbollically?
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