1 Since of the equation is inexact. 7 c) (Sy-2x)y-2y P= -24 9 = (sy-2x); Since oy др = 52²-2xy ye 1 - 0 OP by 09 = To solve the ODE: ↳) (Sy-2x)dy - 2ydx = 0 буду-2xdy-гуах Sydy - 2 ( xdy-yax) = 0 5ydy-2d(xy) 5 Juay - 2jdĺxy) - C ox og the ODE is exact. da Ox C √2 (5+2x²)+2x 5 d) ( ^//t + 1/²-2 1/2- (=) (Sy-2x)day-2ydx = 0 = -2 =-2 which is implicit solution of the ODE. --√2. (SC + 2x²)-2x 5 or y = C'£2.8 199 5 +
1 Since of the equation is inexact. 7 c) (Sy-2x)y-2y P= -24 9 = (sy-2x); Since oy др = 52²-2xy ye 1 - 0 OP by 09 = To solve the ODE: ↳) (Sy-2x)dy - 2ydx = 0 буду-2xdy-гуах Sydy - 2 ( xdy-yax) = 0 5ydy-2d(xy) 5 Juay - 2jdĺxy) - C ox og the ODE is exact. da Ox C √2 (5+2x²)+2x 5 d) ( ^//t + 1/²-2 1/2- (=) (Sy-2x)day-2ydx = 0 = -2 =-2 which is implicit solution of the ODE. --√2. (SC + 2x²)-2x 5 or y = C'£2.8 199 5 +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
I solved the ODE of (5y-2x)y'-2y. Which of my y (last line) ist the correct explicit solution?
Transcribed Image Text:10:04 Fri 17 Mar
S
9 = 3xy
c) (Sy-2x)y -24
P = -24
i
9 = (sy-2x);
др
since oy
ду
Since of the equation is inexact
0p + 응웃
ду
=
52/²-2xy
y =
1
T
ох
ax
5ydy - 2d (xy) = 0
5 √ydy - 2fd(xy) = C
=
d) ( ^//t + 1/² - 24
To solve the ODE:
6) (Sy-2x)dy - 2ydx = 0
Sydy - 2xdy - 2ydx = 0
Sydy - 2 (xdy-yax) = 0
с
I
√2 (5+2x² + 2x
5
- 0 (=) (Sy-2x)dy -2ydx = 0
OP
by
09
2
=
82, the ODE is exact
3y⁰
-2
-2
●●●
or
which is implicit solution of the ODE.
-√2·(5C + 2x²) - 2x
5
y =
+212 199
99%
+:
>
215
+
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