GATE 2023 ES – Question 11
Classify P:$y^{\prime}+x=x\sin y$ and Q:$y^{\prime}+xy=e^x\,y$.
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Correct answer: (B) P nonlinear;Q linear
Explanation
P contains sin y, a nonlinear function of the dependent variable. In Q, the printed right side is $e^x\,y$,so moving it left gives $y^{\prime}+(x-e^x)y=0$,linear in y and its derivative. Thus **B**. The exponent is x only; reading the source as $e^{xy}$ would change the classification.