Math. 401, Sec. 501 Spring, 2006
Homework 6, due March 3
1. [Bush, p. 156, (i) and (ii)] Find the (lowest-order) composite expansion for the solu-
tion of
(a) y00 +y0+y
x+1 =2.
(b) y00 −y0+y
x+1 =2.
In both cases [(a) and (b)] consider
0<1,0<x<1,y(0)=0,y(1)=3.
2. [Bush, p. 156, (iii)–(v)] Find the composite expansion for the solution of
(a) y00 +xy0+y=0,
0<1,2<x<4,y(2)=0,y(4)=1.
(b) y00 −xy0+y=0,
0<1,2<x<4,y(2)=0,y(4)=1.
(c) y00 +xy0+y=0,
0<1,−4<x<−2,y(−4) = 1,y(−2)=0.
Do not work out (c) from the beginning; knowing the answers to (a) and (b), you can
solve (c) in two or three lines by a change of variable.
3. [Bush, p. 172, (i)] y00 −y0+1
y=0,
0<1,0<x<1,y(0)=2,y(1)=1.
4. [Bush, p. 172, (ii)] y00 +y0+ey=0,
0<1,0<x<1,y(0)=1,y(1) = −ln 2.
5. [Logan, p. 69, Ex. 3.2(a)] Find the lowest-order composite expansion for positive .
Compare the result with the exact solution, either numerically or in terms of power
series.
y00 +2y
0+y=0,y(0)=0,y(1)=1.
