Toronto Math Forum
MAT2442018S => MAT244––Home Assignments => Topic started by: Vivian Ngo on April 02, 2018, 06:32:08 PM

Can someone please help me with finding H(x,y) = c for the following system?
dx/dt = y
dy/dt = 2x+y

Can you classify the stationary points of this system?

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

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 $H(x,y)=C$

Thanks!