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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Week 7 problems:" }}{PARA 
0 "" 0 "" {TEXT -1 54 "4.7  p. 191  4, 18, 20   p. 328 12, 19  p. 334 \+
 15, 29" }}{PARA 0 "" 0 "" {TEXT -1 42 "4.8  p. 200  17, 32, 41, 56, 6
5  p. 341  5" }}{PARA 0 "" 0 "" {TEXT -1 38 "4.9  p. 206  11, 22, 24, \+
28  p. 354  7" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "4.7  #11" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "d11:=diff(y(x),x,x)-diff(y(x
),x)+y(x)=sin(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "subs(y
(x)=cos(x),d11);simplify(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 39 "subs(y(x)=exp(2*x)/3,d11a);simplify(\");" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 7 "Solve: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 
"d11aa:=diff(y(x),x,x)-diff(y(x),x)+y(x)=5*sin(x);" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 11 "Too easy:  " }{XPPEDIT 18 0 "y(x)=5*cos(x)" "/-%
\"yG6#%\"xG*&\"\"&\"\"\"-%$cosG6#F&F)" }{TEXT -1 30 ".  The other two \+
are the same." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "d11b:=diff
(y(x),x,x)-diff(y(x),x)+y(x)= sin(x)-3*exp(2*x);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 61 "d11c:=diff(y(x),x,x)-diff(y(x),x)+y(x)= 4*sin
(x)+18*exp(2*x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "subs(y(
x)=4*cos(x)+6*exp(2*x),d11c);simplify(\");" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 34 "4,7  #19  First on the blackboard." }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 25 "p17:=d^2-d-2;factor(p17);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 31 "d19a:=diff(v(x),x)+v(x)=exp(x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "s19a:=dsolve(d19a,v(x));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "d19b:=diff(y(x),x)-2*y(x)=rh
s(s19a);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "dsolve(d19b,y(x
));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "W10:=det(Wronskian([sin(x),c
os(x),tan(x)],x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "simpl
ify(W10,trig);" }}{PARA 11 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 19 "plot(\",x=-1.0..1.);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 95 "So the functions are not linearly independent solutions
 of a 3rd order linear DE           on (" }{XPPEDIT 18 0 "(-Pi/2,Pi/2)
" "6$,$*&%#PiG\"\"\"\"\"#!\"\"F(*&F%F&\"\"#F(" }{TEXT -1 2 ")." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "p. 328  #17" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 74 "d17:=x^3*diff(y(x),x,x,x)-3*x^2*diff(y(x),x,x)
 +6*x*diff(y(x),x)-6*y(x)=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 29 "simplify(subs(y(x)=x^3,d17));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "dsolve(d17,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "Wronskian([x,x^2,x^3],x);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 7 "det(\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "p. \+
334  #1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "dsolve(diff(y(x)
,x,x,x)+2*diff(y(x),x,x) -8*diff(y(x),x),y(x));" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 11 "p. 334  #19" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 102 "i19:=\{diff(y(x),x,x,x)-diff(y(x),x,x) -4*diff(y(x),x) +4*y(x)=
0, y(0)=-4, D(y)(0)=-1, D(D(y))(0)=-19\};" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 17 "dsolve(i19,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "pt3:=diff(y(t),t,t)+2*diff(y(t),t)+5*y(t)=0;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(pt3,y(t));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "sol:=rhs(dsolve(\{pt3,y(0)=0
,D(y)(0)=-1\},y(t)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "d3
:=diff(sol,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(d3,
t);evalf(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot(\{d3,
sol\},t=0..2,color=blue);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
37 "subs(t=(1/2)*arctan(2),sol);evalf(\");" }}{PARA 11 "" 1 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "d1:=diff(y(x),x,x
)+3*y(x)=-9;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "subs(y(x)=-
3,d1); simplify(\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "p. 200  #
31" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "dsolve(diff(y(t),t)-y
(t)=1,y(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "p. 200  #36" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "d36:=diff(y(t),t,t)-y(t)=exp
(t)-exp(-t)+2;\ninits:=y(0)=0,D(y)(0)=0;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "dsolve(\{d36,inits\},y(t));" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 11 "p. 200  #51" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
46 "d51:=diff(x(t),t,t)-5*diff(x(t),t)+2*x(t)=3^t;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 17 "dsolve(d51,x(t));" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 11 "p. 200  #64" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(\{3^t,exp(t*ln(
3))+.1\},t=0..2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "p. 341  #2" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "factor(l^3+l^2-5*l+3);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "dsolve(diff(y(t),t,t)+diff
(y(t),t,t,t) -5*diff(y(t),t)+3*y(t)=exp(-t)+sin(t),y(t));" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 11 "p. 206  #21" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 58 "d21:=x^2*diff(z(x),x,x)-x*diff(z(x),x)+z(x)=x*(1+3/ln
(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(d21,z(x));
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "p. 207  #23  First let's see \+
if Maple can do it all at once!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 50 "d23:=x*diff(y(x),x,x)-(x+1)*diff(y(x),x)+y(x)=x^2;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(d23,y(x));" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 51 "d23a:=diff(y(x),x,x)-(x+1)/x*diff(y(x),x)
+y(x)/x=x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "dsolve(d23a,y
(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "p. 207  #27" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "i27:=\{diff(y(x),x,x)-y(x)=1/x,y(1)
=0,D(y)(1)=-2\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sol27:=
dsolve(i27,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "?Ei;" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(rhs(sol27),x=1..1.5);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Now let's go back to 4.8 and \+
look at  #65:  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "restart:
d65:=diff(y(x),x,x)+2*diff(y(x),x)+5*y(x)= 0;" }}{PARA 11 "" 1 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "s65:=dsolve
(\{d65,y(0)=0,D(y)(0)=1\},y(x));" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "plot([rhs(s65),piecewise(x<.
1,1,0)],x=0..2*Pi,color=[blue,red]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "de:=diff(y(x),x,x)+y(x)
=tan(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dsolve(de,y(x))
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "71 0 0" 
34 }{VIEWOPTS 1 1 0 2 1 1805 }