GATE 2021 ES – Question 30
For dependent y and independent x, classify $dy/dx=x^2y$.
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Show answer and explanation
Correct answer: (A) Linear; (C) First order
Explanation
Rearrange as $y^{\prime}-x^2y=0$,which is linear in y and its derivative. Its highest derivative is first order. Hence select **A, C**. A variable coefficient x² does not make an equation nonlinear in the dependent variable.