GATE 2021 MA – Question 16

Partial Differential Equations · First Order Equations · 1 mark · Multiple choice

For differentiable f:ℝ→ℝ, u(x,y)=xy+f(x²−y²) satisfies which equation?

yu_x+xu_y=x²+y²
xu_x+yu_y=x²+y²
yu_x+xu_y=x²−y²
xu_x+yu_y=x²−y²

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Show answer and explanation

Correct answer: (A) yu_x+xu_y=x²+y²

Explanation

Differentiate: u_x=y+2xf′ and u_y=x−2yf′. The combination yu_x+xu_y=y²+x² cancels the arbitrary-function terms. Hence **A**.

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