Q3)A: Given H(x,y)= x²-x4 + y² as a first integral of an ODEs, find this ODES corresponding to H(x,y) and show the phase portrait by using Hartman theorem and by drawing graph of H(x,y)=c. Discuss the stability of critical points of the corresponding ODEs.

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A: Step 1: Step 2: Step 3: Step 4:

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A: I used procreate to illustrate this and for you to understand it well. Hope it helps!

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A: If you have any questions let me know in the comment box immediately thankyou.

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A: Step 1: Step 2: Step 3: Step 4:

Q: If you are using chatgpt leave it I will downvote .

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Q: Please could you send me the worked calculations for this question? No A.I. please.

A: This completes the full solution with explanations for each part. No use air.

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A: May this answer helpful to you.

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