IGNOU MTE 8 2018 - Find the value of n for which the equation (n - 1)2 uxx - y2n uy

Question

Find the value of n for which the equation (n - 1)² u_xx - y²ⁿu_yy = ny^2n-1 u_y is parabolic or hyperbolic.

13 Feb 2018

Answer :

Word Count : 288

The given equation is: \[ (n - 1)^2 u_{xx} - y^{2n} u_{yy} = n y^{2n-1} u_y \] We need to determine the value of \( n \) for which this equation is parabolic or hyperbolic. To do this, we need to analyze the general form of second-order linear partial differential equations. The general form of a second-order linear PDE is: \[ A u_{xx} + 2B u_{xy} + C u_{yy} = 0 \]

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