GATE 2021 MA – Question 37

Partial Differential Equations · Second Order Equations and Laplace Equation · 2 marks · Multiple choice

For u_xx+4u_xy+(x²+4y²)u_yy=sin(x+y), P:the PDE is parabolic on x²/4+y²=1. Q:it is hyperbolic inside that ellipse. Choose truth values.

Both P and Q true
P true, Q false
P false, Q true
Both false

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Show answer and explanation

Correct answer: (A) Both P and Q true

Explanation

In the convention Au_xx+2Bu_xy+Cu_yy, A=1,B=2,C=x²+4y². Discriminant B²−AC=4−x²−4y² is zero on the ellipse and positive inside. Both claims hold. **A**.

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