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9.2 Question 19

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Vivian Ngo:
Can someone please help me with finding H(x,y) = c for the following system?

dx/dt = y
dy/dt = 2x+y

Victor Ivrii:
Can you classify the stationary points of this system?

Vivian Ngo:
I got that (0,0) is a saddle point and that the general solution is $x(t) =c_{1}e^{2t}[1,2]^T+ c_{2}e^{-t}[1,-1]^T$.

I just can't seem to get an expression of the form H(x,y)=c

Victor Ivrii:
1. Write system as a single equation, excluding $dt$
2. Is it exact?
                 2a. If "yes", then integrate it
                 2b. If "no", find an integrating factor and integrate it
    In both cases you'll get $H(x,y)=C$

Vivian Ngo:
Thanks!

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