GATE CE 2015 Set 1 — Question 38
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Engineering Mathematics → Ordinary Differential Equations → Exact Differential Equations
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Question
Consider the following differential equation:Which of the following is the solution of the above equation ( is an arbitrary constant)?
Correct answer
(C) xy cos (y)/(x) = c
Solution
The given differential equation is:
We can rewrite the differentials as:
Substituting these into the equation:
Divide both sides by :
Rearranging terms:
Let and :
Alternatively, let's check Option C:
Differentiating:
Multiply by :
This matches the original equation. Therefore, Option C is the correct solution.
We can rewrite the differentials as:
Substituting these into the equation:
Divide both sides by :
Rearranging terms:
Let and :
Alternatively, let's check Option C:
Differentiating:
Multiply by :
This matches the original equation. Therefore, Option C is the correct solution.
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