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Question: Solve PDE by pdsolve, how to interpret answer?

Question:Solve PDE by pdsolve, how to interpret answer?

Sannis 10 Maple 16
pde pdsolve
November 28 2016
1

Hi! 

Tried to solve the PDE below (q and p are time-dependent variabels, q(t),p(t)):

pde := diff(rho(t, q, p), t) = -(diff(rho(t, q, p), q))*p+(diff(rho(t, q, p), p))*(2*q+2);
          

pdsolve(pde, rho(t, q, p));

And got the answer: 

rho(t, q, p) = _F1(p^2+2*q^2+4*q, -(1/2)*sqrt(2)*arctan((q+1)*sqrt(2)*(1/sqrt(p^2)))+t)

But I'm not sure how to interpret the result. I understand that  _F1 is an arbitrary function, but then I get confused with the comma? I thought that I'd get a function of q and p, where they depend on t. 

Best regards
Sannis

 
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