GATE 2026 MA – Question 25

Partial Differential Equations · Second Order Equations and Laplace Equation · 1 mark · Multiple select

For distinct a,b > 0, consider $af_{xx}+bf_{yy}=8f$. Which pairs (ξ,η) make $f=e^{2\xi x+\eta y}$ a solution?

Show answer and explanation

Correct answer: (A) $(1/\sqrt a,2/\sqrt b)$; (D) $(0,2\sqrt{2/b})$

Explanation

Substitution gives $4a\xi^2+b\eta^2=8$. A yields 4+4 = 8; B gives 0; C gives 2+1/2 = 2.5; D gives 0+8 = 8. **A,D**.

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