ear differential equation, two functions y, and y2, and a pair of initial conditions are given. First verify that y and y2 are solutions of the differential equation. Then find a particular solution of the form y cy + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. 3. y"+ 4y = y'(0) = 8 4. у" + 25у y'(0) = -10 5. y" - Зу +2у 6. y" +y-6 y'(0) = -1 1. y" - y = 0; y = e*, y2 = e; y(0) = 0, y'(0) = 5 112 Chapter 2 Linear Equations of Higher Order 7. y"+y' 0; y, 1, y2 =e; y(0) = -2, y'(0) 8 8. y"- 3y' 0; y = 1, y2 = e"; y(0) = 4, y'(0) = -2 9. y" + 2y' + y = 0; y, = e, y2 xe; y(0) = 2, y'(0) = -1 10. y" – 10y' + 25y = 0; y = e, y2 = xe"; y(0) = 3, y'(0) = 13 11. y"-2y'+2y 0; y1 = e* cos x, y2 = e" sin x; y(0) = 0, y'(0) = 5 12. y" + 6y +13y 0; y, e-3 cos 2x, y = e- sin 2x; y(0) = 2, y'(0) = 0 13. x'y" 2xy + 2y 0: x, ya x; y(1) = 3, 31. Show that y, dependent fun x 0. Why equation of the p and q contim solutions? %3D %3D %3D %3D 32. Let y and yz C(x)y are continuou W(y, y2). Sh-
ear differential equation, two functions y, and y2, and a pair of initial conditions are given. First verify that y and y2 are solutions of the differential equation. Then find a particular solution of the form y cy + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. 3. y"+ 4y = y'(0) = 8 4. у" + 25у y'(0) = -10 5. y" - Зу +2у 6. y" +y-6 y'(0) = -1 1. y" - y = 0; y = e*, y2 = e; y(0) = 0, y'(0) = 5 112 Chapter 2 Linear Equations of Higher Order 7. y"+y' 0; y, 1, y2 =e; y(0) = -2, y'(0) 8 8. y"- 3y' 0; y = 1, y2 = e"; y(0) = 4, y'(0) = -2 9. y" + 2y' + y = 0; y, = e, y2 xe; y(0) = 2, y'(0) = -1 10. y" – 10y' + 25y = 0; y = e, y2 = xe"; y(0) = 3, y'(0) = 13 11. y"-2y'+2y 0; y1 = e* cos x, y2 = e" sin x; y(0) = 0, y'(0) = 5 12. y" + 6y +13y 0; y, e-3 cos 2x, y = e- sin 2x; y(0) = 2, y'(0) = 0 13. x'y" 2xy + 2y 0: x, ya x; y(1) = 3, 31. Show that y, dependent fun x 0. Why equation of the p and q contim solutions? %3D %3D %3D %3D 32. Let y and yz C(x)y are continuou W(y, y2). Sh-
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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please send handwritten solution for Q 12
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Transcribed Image Text:ear differential equation, two functions y, and y2, and a pair
of initial conditions are given. First verify that y and yz are
solutions of the differential equation. Then find a particular
solution of the form y = cy + czy2 that satisfies the given
initial conditions. Primes denote derivatives with respect to x.
3. у" + 4y
y'(0) = 8
4. y" + 25y
y'(0) = -10
5. y"- Зу +2у
6. y" +y-6
y'(0) = -1
%3D
1. y" - y = 0; y, = e*, y2 = e; y(0) = 0, y'(0) = 5
%3D
112
Chapter 2 Linear Equations of Higher Order
7. y" +y' 0; y = 1, y2 =e; y(0) = -2, y'(0) = 8
8. y" - 3y' 0; y 1, y2 = e; y(0) = 4, y'(0) = -2
9. y" + 2y' +y = 0; y = e, y2 xe; y(0) = 2,
y'(0) = -1
10. y" - 10y' + 25y 0; y e, y = xe; y(0) = 3,
y'(0) = 13
11. y"- 2y'+2y = 0; y = e" cos x, yz = e" sin x; y(0) = 0,
y'(0) = 5
12. y"+ 6y + 13y 0; y = e-3 cos 2x, y2 e-3t sin 2x;
y(0) = 2, y'(0) = 0
13. x*y" - 2xy' + 2y 0: x, ya x; y(1) = 3,
y'(1) = 1
14. x'y"+2xy'-6y = 0; y = x, yz = x-; y(2)
У (2) %3 15
15. x?y" - xy' + y = 0; yi = x, y2 = x In x; y(1) = 7,
y'(1) = 2
16. x?y" + xy' + y = 0; y
y(1) = 2, y'(1) = 3
31. Show that yı
dependent fun
x = 0. Why
equation of the
p and q contim
solutions?
%3D
%3D
%3D
%3D
32. Let y and yz
C(x)y = 0 c
are continuou:
W(y, y2). She
%3D
%3D
%3D
= 10,
A(x
%3D
%3D
Then substitut
ential equation
= cos(ln x), y2 = sin(In x);
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