The one dimensional heat conduction partial differential rquation
$\frac{\partial T}{\partial t} = \frac{\partial^{2} T}{\partial x^{2}}$ , is

Parabolic

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Hyperbolic

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Elliptic

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Mixed

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Solution

The correct option is A Parabolic
$\frac{\partial T}{\partial t} = \frac{\partial^{2} T}{\partial x^{2}}$ ........ (i)
Comparing (i) with
$A \frac{\partial^{2} T}{\partial x^{2}} + B \frac{\partial^{2} T}{\partial x \partial y} + C \frac{\partial^{2} T}{\partial y^{2}} + 2 G \frac{\partial T}{\partial x} + 2 F \frac{\partial T}{\partial y} + H = 0$
$A = 1, B = 0, C = 0$
$∵ B^{2} - 4 A C = 0$
$\Rightarrow$ Parabolic Partial Differential Equation

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The one dimensional heat conduction partial differential rquation ∂T∂t=∂2T∂x2, is

The correct option is A Parabolic∂T∂t=∂2T∂x2 ........ (i) Comparing (i) with A∂2T∂x2+B∂2T∂x∂y+C∂2T∂y2+2G∂T∂x+2F∂T∂y+H=0 A=1,B=0,C=0 ∵B2−4AC=0 ⇒ Parabolic Partial Differential Equation

The one dimensional heat conduction partial differential rquation
$\frac{\partial T}{\partial t} = \frac{\partial^{2} T}{\partial x^{2}}$ , is