20. y"-4y + 3y = x; y1 = e
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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4.3 HOMOGENEOUS LINEAR
15. (1 2x- x)y + 2(1 + x)y'- 2y 0; yı =x+1
16. (1 – x)y" + 2xy = 0;
y = 1
In Problems 17-20 the indicated function yı(x) is a solution
of the associated homogeneous equation. Use the method
of reduction of order to find a second solution y(x) of the
22.
homogeneous equation and a particular solution of the given
nonhomogeneous equation.
17. y" – 4y = 2; yı = e *
18. y+y I; y = 1
Con
19. v"- 3y + 2y = 5e y=e
20. y"- 4y +3y = x y = e
23.
Discussion Problems
21. (a) Give a convincing demonstration that the becond-
order equation ay"+ by +ey 0, a, b, and e con-
stants, always possesses at least one solution of the
= m, a constant.
form y
(b) Explain why the differential equation in part (a)
must then have a second solution either of the form
4.3
HOMOGENEOUS LINCAD
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