2. Obtain the general solution of the following equations: (i) x²uxx + 2xyuxy + y²uyy + xyux + y² uy = 0,
2. Obtain the general solution of the following equations: (i) x²uxx + 2xyuxy + y²uyy + xyux + y² uy = 0,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Obtain the general solution of the following equations:
(i) x² Uxx + 2xyuxy + y²uyy + xyux + y² uy = 0,
c²rurr-2c²ur
(ii) rutt - c²rurr - 2c² ur
= 0, c = constant,
(iii) 4ux + 12xy +9uyy - 9u = 9,
(iv) Uxx + Uxy - 2Uyy - 3ux6uy = 9 (2x - y),
(v) yux+3y Uxy + 3ux = 0,
y = 0.
(vi) Uxx + Uyy
(vii) 4uxx + Uyy = 0,
(viii) Uxx
+ Uyy
(ix) 2 Uxx + Uyy = 0,
(x) U+Aury+4uyy =0,
(xi) 3ur +4ury — huy
-
= 0,
-2ury
= = 0,
= 0.
=
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