GATE 2026 AG – Question 11
Identify these PDEs in order, where $c$ is constant:$$(i)\quad \frac{\partial^2u_1}{\partial t^2}=c^2\frac{\partial^2u_1}{\partial x^2},\qquad(ii)\quad \frac{\partial u_1}{\partial t}=c^2\frac{\partial^2u_1}{\partial x^2},\qquad(iii)\quad \frac{\partial^2u_2}{\partial x^2}+\frac{\partial^2u_2}{\partial y^2}=0.$$
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Correct answer: (A) Wave;Heat;Laplace
Explanation
Equation (i) has a second time derivative equated to a second spatial derivative:the wave equation. Equation (ii) has a first time derivative with spatial diffusion:the heat equation. Equation (iii) states that the spatial Laplacian vanishes:Laplace’s equation. The ordered identification is **A**.