Find the solution of the following Differential Equations I) ydr + xdy =0 3) (2x+e' )dx + xe' dy 0 2) (xdy - yde)/x =0 4) 2x In(y)dr + y"x'dy 0
Find the solution of the following Differential Equations I) ydr + xdy =0 3) (2x+e' )dx + xe' dy 0 2) (xdy - yde)/x =0 4) 2x In(y)dr + y"x'dy 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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Question
Transcribed Image Text:1 %TA l. , * 0
** h. e
శికి 1:1b
A 195 Partial differtial..→:
JSx)dx = J =dx = In(x)
Multiplying both sides of the equation by the integrating factor p(x) =x, we get
x(2 ydx + xdy)= 0 = 2xydx + x'dy 0
which is exact because
- 2x and
= 2x, and the solution is
S(x, y) = [2xydx x'y+g(y)
r'y+g)-x +g'0)
+g'(y) =x = g'0)-D0
g(9)-fgdy-C ry-C
Mathematics
Electrical & Electronic Engineering Department
Sd Year
Dr. Atheer AliSahr
Exercises
Find the solution of the following Differential Equations
2) (xdy- ydx)/ x' =0
4) 2x In(y)dx+ yr'dy 0
I) ydr + xdy =0
3) (2x+e' )dx + xe' dy = 0
5) sinh(x)cos(y)dx cosh(x)sin(y)dy
6) 3re"d0+e"dr = 0
7) (1+x')dy +2.xydx 0
8) xdy -4ydx =0
9) ydr + x(1+ y)dy =0
10) (2ydx+ dy)e" =0
11) (3y cos(3x)dx-sin(3x)dy)/ y =0
12) sin(By)dx =-ß cos(B y)dy
13) xdy - ydx =0
14) 2cos(r y)dx =r sin(7 y)dy
15) ycos(x)dx+ 3sin(x)dy = 0
16) 3ydr +2xdy =0
17) dr+(y/x)'dy =0
18) 2dx-e"dy =0
19) ycos(x)dx+ 2sin(x)dy = 0
20) (y+)dx-(x+1)dy =0
21) 2ydx +x
22) sin(y)dx + cos(y)dy = 0
23) 2dx + sec(x)cos(y) =0, y(0) 0
24) 2x'dx - 3xy'dy = 0, y(1) =0
25) 2 sin( y)dx + cos(y )dy = 0,
26) (2y + xy)dx + 2xdy = 0.
y(0) =/2
y(3) = /2
ضحی عمار خلف
12:10 äclull 21.02.26
II
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