GATE CE 2024 Set 2 — Question 15
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Engineering Mathematics → Ordinary Differential Equations → Exact Differential Equations
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Question
Consider two Ordinary Differential Equations (ODEs):P: Q: Which one of the following options is CORRECT?
Correct answer
(B) P is a homogeneous ODE and Q is not an exact ODE.
Solution
Analysis of ODE P:
Since , P is a homogeneous ODE.Analysis of ODE Q:
This is in the form , where and .
Check for exactness: and .
Since , the ODE is not exact.Conclusion: P is homogeneous and Q is not exact. Correct option is (B).
Since , P is a homogeneous ODE.Analysis of ODE Q:
This is in the form , where and .
Check for exactness: and .
Since , the ODE is not exact.Conclusion: P is homogeneous and Q is not exact. Correct option is (B).
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