GATE 2023 MA – Question 26

Partial Differential Equations · Heat and Wave Equations · 1 mark · Numerical answer

For c>0, u_xx−u_tt/c²=0 on ℝ×(0,∞), with u(x,0)=sin x and u_t(x,0)=cos x. The dependence interval for P=(3,2) has endpoints Q,R on the x-axis. If triangle PQR has area 8, find c².

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Correct answer: 4 to 4

Explanation

Characteristics through P meet t=0 at x=3±2c. Base QR=4c and height=2, so area=(1/2)(4c)(2)=4c=8. Hence c=2 and **c²=4**.

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