A.9.1: Section 9.1 Answers
( \newcommand{\kernel}{\mathrm{null}\,}\)
2. y=2x2−3x3+1x
3. y=2ex+3e−x−e2x+e−3x
4. yi=(x−x0)i−1(i−1)!,1≤i≤n
5.
b. y1=−12x3+x2+12x,y2=13x2−13x,y3=14x3−13x2+112x
c. y=k0y1+k1y2+k2y3
7. 2e−x2
8. √2Kcosx
9.
a. W(x)=2e3x
d. y=ex(c1+c2x+c3x2)
10.
- 2
- −e3x
- 4
- 4/x2
- 1
- 2x
- 2/x2
- ex(x2−2x+2)
- −240/x5
- 6e2x(2x−1)
- −128x
24.
- y‴=0
- xy‴−y″−xy′+y=0
- (2x−3)y‴−2y″−(2x−5)y′=0
- (x2−2x+2)y‴−x2y″+2xy′−2y=0
- x3y‴+x2y″−2xy′+2y=9
- (3x−1)y‴−(12x−1)y″+9(x+1)y′−9y=0
- x4y(4)+5x3y‴−3x2y″−6xy′+6y=0
- x4y(4)+3x2y‴−x2y″+2xy′−2y=0
- (2x−1)y(4)−4xy‴+(5−2x)y″+4xy′−4y=0
- xy(4)−y‴−4xy″+4y′=0