Show that u(x, y) = x"f(t), t = y/x, satisfies the differential equations ?u ди + дх ду (a) x- хо (b) ҳаи + 2ху Ju + дхду = n(n − 1)u дуг Verify these results for the function u(x, y) = x³ + y* + 16х²у². = nu
Show that u(x, y) = x"f(t), t = y/x, satisfies the differential equations ?u ди + дх ду (a) x- хо (b) ҳаи + 2ху Ju + дхду = n(n − 1)u дуг Verify these results for the function u(x, y) = x³ + y* + 16х²у². = nu
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:3.7
Show that u(x, y) = x"f(t), t=y/x, satisfies the
differential equations
(а) хан+у
ди
x +y = nu
ду
Fu
Fu
2
du
(b) x² + 2ху
+
= n(n − 1)u
2
dx²
?х у
ду²
Verify these results for the function
u(x, y) = x4 + y4 + 16x²y2.
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