з хутуг х2 +xy dy + ax = 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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no need to solve. just write everything digitally. thank you. i will upvote
Transcribed Image Text:Given:
dy + 3xy ty = 0
xy
=> day
бус х
- (3xy + y²)
xy
Fax (371)
=>dx (-3 xy + y²) = dy (-X² - xy)
→dx (-3 x (x) ³²+ (ux)² = (udx+xdv) (-x²-x²²² (Ux))
=> -3 x² u dx + ²x² dx = -x² udx - x² v² dx - x³ du- x³dv
(+x²udx) (²x) (+ x² udx) (+ x² u²dx)
=>
- [ 2x²udx + 2√³x²dx = -x ³du -x³udu
=> 2x²xdx = 2√³²x²dx = X du txodu
x3
=> 2x²dx-2ux² dx
=> (2x² = x²) dx = 2
f 1 d
X
=
In x
y = x; dy= udx + xdu
dx = f == du
Đinx nu c
In u
=> e
= e
=> X = UC
2 du
du + du
du J-²1
=)/x = C
1
Zu
y=vx
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