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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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