Complex Variables and Partial Differential Equations (3130005)

Question-4c ( i )-OR

BE | Semester-3 Summer-2020 | 27-10-2020

Q4) (c ( i ))

Solve the PDE $(D^{2} - D'^{2} + D - D') z = 0$ .

Here,

(D^{2} - D'^{2} + D - D') z = 0

f (D, D') = (D^{2} - D'^{2} + D - D') = (D - D') (D + D') + (D - D') = (D + D' + 1) (D - D')

i.e.

m_{1} = 1, m_{2} = - 1, α_{1} = 0, α_{1} = - 1 .

Solution:

z = f_{1} (y + x) + e^{- x} f_{2} (y - x)

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