7. y' cosh 5.13x8. y" =-0.279-15VERIFICATION. INITIAL VALUEPROBLEM (IVP)19(a) Verify that y is a solution of the ODE. (b) Determinefrom y the particular solution of the IVP. (c) Graph thesolution of the IVP.9. y' + 4y10. y' + 5xy1.4,-4.c+ 0.35, y(0) = 2= ce , y(0) Ty = ce= 0, y-2.511. y' = y + e*, y= (x + c)e". y(0) =12. yy' = 4x, y- 4x2 = c (y > 0), y(1) = 4113. y' = y- y.y =y(0) 0.2514. y' tan x = 2y - 8, y = c sin2 x + 4, yT) = 0%3D1 Find two constant solutions of the ODE in Prob. 13 byinspection.prFi16. Singular solution. An ODE may sometimes have anadditional solution that cannot be obtained from theinftogeneral solution and is then called a singular solution.The ODE y2 - xy' +y = 0 is of this kind. ShowVothatby differentiation and substitution that it has thewithaeneral solutionv=2and the singular solutionマ+F3F4F5F6F7F8F92324

The following IVP solution has been obtained and verified and graph has been drawn.

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

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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

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