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Engineering Mathematics Miscellaneous

Engineering Mathematics

  1. The partial differential equation
    δu
    + u
    δu
    =
    δ2u
    is
    δtδxδx2
    1. linear equation of order 2
    2. non-linear equation of order 1
    3. linear equation of order 1
    4. non-linear equation of order 2
Correct Option: D

Order is index of a derivative present in a PDE (i.e.) maximum there.

Hence,
δ2u
⇒ highest index 2 ⇒ order = 2
δn2

if y, y2 solution of a PDE, then PDE is linearly independent.
δy1
+
y1δy1
=
δy12
......(1)
δtδxδx2

δy2
+
y2δy2
=
δ2y2
......(2)
δtδxδx2

If y = ay1 + a1 y2 is a sum of the PDE
δ
(ay1 + a1y1) + (ay1 + a2y2)
δ
(ay1 + ay2) =
δ2
(ay1 + ay2)
δtd2d22

Hence PDE is non linear of order 2



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