at all. SECTION 1.2 EXERCISES In Probiems i-10 determine a region of the xy-plane for which the given differential equation would have a unique solution through a point (Xp, yo} firSt in the region. dy dy 2. dx dy dx dy 4. dx
at all. SECTION 1.2 EXERCISES In Probiems i-10 determine a region of the xy-plane for which the given differential equation would have a unique solution through a point (Xp, yo} firSt in the region. dy dy 2. dx dy dx dy 4. dx
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:at all.
SECTION T.2 EXERCISES
as
In Probiems 1-10 determine a region of the xy-plane for which the given
differential equation would have a unique solution through a point (X,, Yo}
in the region.
h ax
2.
Vxy
dy
y
dx
dy
%3D
dx
Transcribed Image Text:iven differential equation. In some cases assume an appropriate interval
al equation xy(9) – xy" + 4xy'-3y = 0
nt we have
n function
al with sys
x? dy + (y-xy - xe) dx = 0
d'y
+ 9y =
= sin y
6.
more unkno
and y den
dy
following
1
dr?
d'y
dx
d'r
8.
= -
dx
dr?
(sin x)y" - (cos x)y'
Problems 11-40 verify that the indicated function is a solution of the
= 2
10. (1- y?) dx + x dy = 0
validity for the solution. Where used, the symbols c, and c, denote con-
ants.
1. 2y' +y = 0; y e-2
12. y' + 4y = 32; y = 8
ple functid
dy
tem on soi
2y e: y = er + 10e?*
dx
dy
14.
+ 20y = 24; y = - e-01
dt
y' = 25 + y; y = 5 tan 5x
dy
: y= (Vx + c), x > 0, c > 0
V x
dx
ations are
o need to . y' + y = sin x; y = sin x- cos x + 10e *
erms of
*. B. 2xy dx + (x + 2y) dy = 0; x'y + y =
er y in term
nd
20 (y') + xy' = y; y = x+ 1
1
e differentio. x dy + 2xy dx = 0; y =
example. A
fferentiab1. y = 2xy' + y(y')': y? = c(x + c;)
ve may r2. y' = 2Viyl: y = xx
algebra.
icit solutid3. y'
y = 1; y=x In x, x>0
- -
quation f
of symb4.
aC;e
1+ bcet
2- X
dP
P(a -- bP); P =
dt
dX
5.
dt
3(2-X)(1-X); in
1 -
n is linc, y' + 2xy = 1; y=eedt + ce
+Ge
On is lined,
= 0: C(x +y) = re
7. (x+ y) dx + (x - xy) dy
y = 0 8. y" + y'- 12y = 0; y Ce+ Ce
9. y" - 6y' + 13y = 0; y = e cos 2x
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