9-15 VERIFICATION. INITIAL VALUE PROBLEM (IVP) (a) Verify that y is a solution of the ODE. (b) Determine from y the particular solution of the IVP. (c) Graph the solution of the IVP. 9. y' + 4y = 1.4, 10. y' + 5xy = 0, y= ce 11. y' y + e“, y (x+ c)e", y(0) = 12. yy' = 4x, y y = ce 4 + 0.35, y(0) 2 %3D e-2.5 -2.5 y(0) 7 %3D 4x = c(y > 0), y(1) = 4 1 13. y' y-y, y = y(0) 0.25 %3D 14. y' tan x 2y – 8, y = c sin2x+4, y7) = 0 y = c sin2 x + 4, y(7) = 0 %3D 1. Find two constant solutions of the ODE in Prob. 13 by inspection. 16. Singular solution. An ODE may sometimes have an additional solution that cannot be obtained from the general solution and is then called a singular solution. The ODE y2 - xy' + y = 0 is of this kind. Show
9-15 VERIFICATION. INITIAL VALUE PROBLEM (IVP) (a) Verify that y is a solution of the ODE. (b) Determine from y the particular solution of the IVP. (c) Graph the solution of the IVP. 9. y' + 4y = 1.4, 10. y' + 5xy = 0, y= ce 11. y' y + e“, y (x+ c)e", y(0) = 12. yy' = 4x, y y = ce 4 + 0.35, y(0) 2 %3D e-2.5 -2.5 y(0) 7 %3D 4x = c(y > 0), y(1) = 4 1 13. y' y-y, y = y(0) 0.25 %3D 14. y' tan x 2y – 8, y = c sin2x+4, y7) = 0 y = c sin2 x + 4, y(7) = 0 %3D 1. Find two constant solutions of the ODE in Prob. 13 by inspection. 16. Singular solution. An ODE may sometimes have an additional solution that cannot be obtained from the general solution and is then called a singular solution. The ODE y2 - xy' + y = 0 is of this kind. Show
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
![7. y' cosh 5.13x
8. y" =
-0.27
9-15
VERIFICATION. INITIAL VALUE
PROBLEM (IVP)
19
(a) Verify that y is a solution of the ODE. (b) Determine
from y the particular solution of the IVP. (c) Graph the
solution of the IVP.
9. y' + 4y
10. y' + 5xy
1.4,
-4.c
+ 0.35, y(0) = 2
= ce , y(0) T
y = ce
= 0, y
-2.5
11. y' = y + e*, y= (x + c)e". y(0) =
12. yy' = 4x, y- 4x2 = c (y > 0), y(1) = 4
1
13. y' = y- y.
y =
y(0) 0.25
14. y' tan x = 2y - 8, y = c sin2 x + 4, yT) = 0
%3D
1 Find two constant solutions of the ODE in Prob. 13 by
inspection.
pr
Fi
16. Singular solution. An ODE may sometimes have an
additional solution that cannot be obtained from the
inf
to
general solution and is then called a singular solution.
The ODE y2 - xy' +y = 0 is of this kind. Show
Vo
that
by differentiation and substitution that it has the
with
aeneral solutionv=
2and the singular solution
マ+
F3
F4
F5
F6
F7
F8
F9
23
24](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0aec16c8-71f0-4911-9562-2e6b5b636283%2F38d040f0-b400-4a00-9a0b-5709af19ab76%2Fhmtpz3e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. y' cosh 5.13x
8. y" =
-0.27
9-15
VERIFICATION. INITIAL VALUE
PROBLEM (IVP)
19
(a) Verify that y is a solution of the ODE. (b) Determine
from y the particular solution of the IVP. (c) Graph the
solution of the IVP.
9. y' + 4y
10. y' + 5xy
1.4,
-4.c
+ 0.35, y(0) = 2
= ce , y(0) T
y = ce
= 0, y
-2.5
11. y' = y + e*, y= (x + c)e". y(0) =
12. yy' = 4x, y- 4x2 = c (y > 0), y(1) = 4
1
13. y' = y- y.
y =
y(0) 0.25
14. y' tan x = 2y - 8, y = c sin2 x + 4, yT) = 0
%3D
1 Find two constant solutions of the ODE in Prob. 13 by
inspection.
pr
Fi
16. Singular solution. An ODE may sometimes have an
additional solution that cannot be obtained from the
inf
to
general solution and is then called a singular solution.
The ODE y2 - xy' +y = 0 is of this kind. Show
Vo
that
by differentiation and substitution that it has the
with
aeneral solutionv=
2and the singular solution
マ+
F3
F4
F5
F6
F7
F8
F9
23
24
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