$Linear solutions, linear systems, autonomous systems, and key points.$

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Answer all questions with all work shown.

Ordinary Differential Equations Systems of Linear Equations

Bunbun

Matchmaticians Linear solutions, linear systems, autonomous systems, and key points. File #1

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Please find the attachment. Q8 part c is unclear they want to solve for x(t) and y(t) because I already solved for y(x) which is also the solution of the DE.
Integral curves is also unclear at this point for the same.

Trajectory plot for 8b added. And part c solution is the same as part b, because integral curves here is the solution of differential equation involving dy/dx.

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Aman R

Bunbun

Meeting with my prof today and will ask about that question.
Bunbun

I can't attach a picture to this solution, so I'll make a new question just so I can attach the related concepts and examples from the textbook. Hope they help.
Aman R

I think it's better if you email matchmatician regarding your concern. I am sure there is a way and they will guide you
Aman R

I looked at your examples and realised solving phase plane equation yields the same solution by solving for y(X) or an implicit equation involving X and y together. What else extra needs to be added is graph of the solution which is called the trajectory. I will add the graph today. And answer of part c) is same as part b)
Bunbun

Thanks. Glad the examples helped

$Linear solutions, linear systems, autonomous systems, and key points.$

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