Toronto Math Forum

MAT244-2018S => MAT244––Home Assignments => Topic started by: Vivian Ngo on April 02, 2018, 06:32:08 PM

Title: 9.2 Question 19
Post 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

Title: Re: 9.2 Question 19
Post by: Victor Ivrii on April 02, 2018, 08:29:37 PM

Can you classify the stationary points of this system?

Title: Re: 9.2 Question 19
Post by: Vivian Ngo on April 02, 2018, 11:26:35 PM

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

Title: Re: 9.2 Question 19
Post by: Victor Ivrii on April 03, 2018, 02:20:32 AM

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 $H(x,y)=C$

Title: Re: 9.2 Question 19
Post by: Vivian Ngo on April 03, 2018, 10:32:42 AM

Thanks!