Example 11.1. Classify the following equations : au a²u d²u du (i) +4 0x2 +4 Əxdy 2 ông Ôx ди +2- = 0 dy o²u 2 a²u (ii) x² + (1 - y²) = əx² :0, -∞ < x ∞, -1
Example 11.1. Classify the following equations : au a²u d²u du (i) +4 0x2 +4 Əxdy 2 ông Ôx ди +2- = 0 dy o²u 2 a²u (ii) x² + (1 - y²) = əx² :0, -∞ < x ∞, -1
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:Example 11.1. Classify the following equations :
a²u
22u
d²u du
du
+4.
+4
J
+ 2-
= 0
Əxdy
oy² ax
dy
a²u
•+ (1 - y²¹).
= 0, -∞ < x ∞, -1 <y<1
d'u
·0.
+ (4 + x²) 0² u
əxôt
at
0x2
(ii) x² d²u.
0x2
(iii) (1 + x² ) ª²u
Əx
Oy 2
+ (5 + 2x²).
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