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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "p. 52  14, 25, 28, 30, 35,
 37" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "d14:=x*diff(y(x),x)+
3*y(x)+2*x^2=x^3+4*x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "ds
olve(d14,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "d25:=dif
f(y(x),x)+2*x*y(x)=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "in
tfac:=exp(int(2*x,x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "d
25m:=intfac*d25;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "int(lhs
(d25m),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "So Maple doesn't se
em to help.  However, Maple can do it..." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "dsolve(\{d25,y(2)=1\},y(x));" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 39 "To work the problem just do it by hand." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "d28:=diff(y(x),x)+y(x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "subs(y(x)=exp(-x),d28); simplify(%)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "subs(y(x)=C*exp(-x),d2
8); simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "d30:=di
ff(y(x),x)+2*y(x)=x*y(x)^(-2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 "subs(y(x)=v(x)^(1/3),d30);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "d30l:=v(x)^(2/3)*%;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "dsolve(d30l,v(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "s
ubs(v(x)=y(x)^3,%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Comments o
n mixing problems in general. . . in class." }}{PARA 0 "" 0 "" {TEXT 
-1 52 "35 a.  Let A(t) be the mass of the salt in the tank." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "d35a:=diff(A(t),t)=2*5-A(t)/
500*5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "init:=A(0)=50;" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "s35a:=dsolve(\{d35a,init\}
,A(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(rhs(s35a),t
=0..1000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "a10:=evalf(su
bs(t=10,rhs(s35a)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "d35
b:=diff(A(t),t)=2*5-A(t)/(500-(t))*6;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 84 "d35f:=diff(A(t),t) +6*A(t)/(500-t)=10;\nif35:=exp(int
(6/(500-t),t));\nd35e:=d35f*if35;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "d35h:=simplify(d35e);initb:=A(0)=a10;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "s35b:=dsolve(\{d35e,initb\},A(t));
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "evalf(subs(t=20,rhs(s35
b))/(500-20*1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "ea:=(51
0-t)*(2/(510-t)^5+C);\nsolve(subs(t=10,ea)=a10,C);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 13 "subs(C=%,ea);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "subs(t=30,%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 6 "%/480;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "plot(rhs(s
35b),t=0..499.9,A=0..600,numpoints=1000);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 49 "d37:=diff(x(t),t)=alpha-beta*cos(Pi*t/12)-k*x(t);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "dsolve(\{d37,x(0)=xo\},x(
t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "subs(\{alpha=1,beta
=1,k=2,xo=10\},%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(
rhs(%),t=0..24);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "int(cos
(x)*cos(y)+2*x,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(
%+c(y),y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "dsolve(%=-sin
(x)*sin(y)-2*y,c(y));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "F:
=(t,y)->y*exp(t)+y-t*exp(t)+exp(t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "diff(F(t,y),t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "diff(F(t,y),y);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 53 "dsolve(diff(y(t),t)*(1+exp(t))+exp(t)*(y(t)-t),y(t));
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "degomp:=diff(P(t),t)=P(
t)*(a-b*ln(P(t)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "solg:
=dsolve(\{degomp, P(0)=76\},P(t));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 58 "subs(\{a = .1972285578e-1, b = .1314857052e-2\}, rhs(
solg));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(%,t=0..100)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "fsolve(\{b=a/15, subs(
t=90,rhs(solg))=250\},\{a,b\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{MARK "52" 0 }{VIEWOPTS 1 1 0 2 1 1805 }