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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
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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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. =
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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