GATE EC 2018 Set 1 — Question 44
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Engineering Mathematics → Differential Equations → First-Order Nonlinear Equations
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Question
A curve passes through the point and satisfies the differential equationThe equation that describes the curve is
Correct answer
(A) ln(1 + (y²)/(x²)) = x - 1
Solution
The given differential equation is . Rearranging, we get . Let , then . Substituting these into the equation: . This is a linear differential equation with integrating factor . The solution is . Thus, . Taking the natural logarithm: . Since the curve passes through , we have . Therefore, the equation is .
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