GATE 2022 MA – Question 35

Partial Differential Equations · Second Order Equations and Laplace Equation · 1 mark · Numerical answer

Transform 7u_xx+16u_xy+4u_yy=0 using ξ=y−2x,η=7y−2x into Au_ξξ+Bu_ξη+Cu_ηη=0. Find (B²−4AC)/12³.

Show answer and explanation

Correct answer: 12 to 12

Explanation

Chain rule gives ∂x=−2∂ξ−2∂η and ∂y=∂ξ+7∂η. Therefore A=28−32+4=0,C=28−224+196=0, and B=56−256+56=−144. The requested value is 144²/1728=**12**.

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