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NonLinear ODE Questionby fzksfun
Tags: nonlinear 
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#1
Jan2309, 01:44 PM

P: 3

Hey Guys,
I am really confused about the first problem on my first problem set in Diff Eq (not auspicious is it? Oh well...) Draw the Direction field y' = y y^2. Identify Isoclines and any equlibrium solutions. I don't understand how to approach this problem because doesn't the y^2 term make the equation nonlinear? Also, my professor mentioned that equilibrium solutions could be stable or unstable without telling us what that entailed so can you guys please enlighten me with that , also? Thank you so much in advance. 


#2
Jan2309, 02:17 PM

P: 626

You should be able to read your book to find that to figure out eq. points, you set your y' = 0 and solve. Then there's a variety of ways to figure out stability, you can plot your f(y) = y  y^2 and then obviously where it crosses the horizontal axis, those are your fixed points. When your graph is above the horiz. axis, draw an arrow point right ">" when it's below, draw an arrow point left "<". Now if both your arrows point towards your fixed point then it's stable, otherwise unstable. You can also find f'(y) and plug in your fixed points.



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