IGNOU MTE 8 2018 - Solve the following PDEs:i) ). (3D2 - 2D2 + D - 1)Z = 4ex+yii)

Question

Solve the following PDEs:

i) ). (3D² - 2D² + D - 1)Z = 4e^x+y

ii) (D + D² - 1) (D + 2D' - 3) Z = 4 + 3X + 6Y.

13 Feb 2018

Answer :

Word Count : 258

To solve the given partial differential equations (PDEs), we'll approach each one using standard numerical methods. ### Problem i: \[ (3D^2 - 2D^2 + D - 1)Z = 4e^{x+y} \] Solution Approach: 1. Simplify the left-hand side of the equation first. 2. The operator `D` is typically the differential operator with respect to a variable. We will assume that `D` corresponds to the differentiation with respect to `x`, and the equation involves second derivatives. Thus, we rewrite the equation as: \[ (3\frac{\partial^2}{\partial x^2} - 2\frac{\partial^2}{\partial y^2} + \frac{\partial}{\partial

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