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Question: how to solve this equation

Question:how to solve this equation

LeeHoYeung 535 Maple
physics
October 15 2015
0

H := 1/(2*m)*diff(f(q,P,t), q)^2 = -diff(f(q,P,t),t);
assume f = f1(q) + f2(t);
H := 1/(2*m)*diff(f1(q), q)^2 = -diff(f2(t),t);
dsolve(H);

set each side of equation be a constant E which is anticipated integration constant
how to solve to S = q*sqrt(2*m*E) - E*t

and

p = diff(S,q) = sqrt(2*m*E);
Q = diff(S,E) = q*m/sqrt(2*m*E) - t;
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