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GATE 2017 CE (CE1) – Question 30

Engineering Mathematics · PDE: Fourier series, separation of variables, diffusion, wave and Laplace equations · 1 mark · Numerical answer

For the PDE $$3\frac{\partial^2\phi}{\partial x^2}+B\frac{\partial^2\phi}{\partial x\partial y}+3\frac{\partial^2\phi}{\partial y^2}+4\phi=0,$$ find $B^2$ for a parabolic equation.

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Correct answer: 35.9 to 36.1

Explanation

For $A\phi_{xx}+B\phi_{xy}+C\phi_{yy}+\cdots=0$, the discriminant is $B^2-4AC$. A parabolic equation has zero discriminant. Here $A=C=3$, so $B^2=4(3)(3)=36$. The zeroth-order term $4\phi$ does not affect classification.

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