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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Exercises assigned:" }}
{PARA 0 "" 0 "" {TEXT -1 11 "1.4   5, 12" }}{PARA 0 "" 0 "" {TEXT -1 
32 "2.1, 2.2   3, 12, 23, 27, 29, 32" }}{PARA 0 "" 0 "" {TEXT -1 28 "2
.3   10, 14, 25, 29, 32, 36" }}{PARA 0 "" 0 "" {TEXT -1 24 "2.4   2, 4
, 6, 8, 22, 31" }}{PARA 0 "" 0 "" {TEXT -1 43 "Exam Friday (19 Sept) o
ver 1.1 through 2.4." }}{PARA 0 "" 0 "" {TEXT -1 74 "Today p. 63  1, 3
, 5, 7, 21, 29, (32 <- Orthogonal trajectories Wednesday)" }}{PARA 0 "
" 0 "" {TEXT -1 77 "                      ^classify, ^    ^show not ex
act, y^(-2) an integ factor" }}{PARA 0 "" 0 "" {TEXT -1 46 "          \+
                             | solve" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 4 "1.  " }{XPPEDIT 18 0 "(x^2*y+x^2*cos(x))*dx-x^3*dy=0" "/,&*&,&*&
%\"xG\"\"#%\"yG\"\"\"F**&F'\"\"#-%$cosG6#F'F*F*F*%#dxGF*F**&F'\"\"$%#d
yGF*!\"\"\"\"!" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "3.  " }
{XPPEDIT 18 0 "(y*exp(x*y)+2*x)*dx+(x*exp(x*y)-2*y)*dy=0" "/,&*&,&*&%
\"yG\"\"\"-%$expG6#*&%\"xGF(F'F(F(F(*&\"\"#F(F-F(F(F(%#dxGF(F(*&,&*&F-
F(-F*6#*&F-F(F'F(F(F(*&\"\"#F(F'F(!\"\"F(%#dyGF(F(\"\"!" }{TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 4 "5.  " }{XPPEDIT 18 0 "y^2*dx+(2*x*y+co
s(y))*dy" ",&*&%\"yG\"\"#%#dxG\"\"\"F'*&,&*(\"\"#F'%\"xGF'F$F'F'-%$cos
G6#F$F'F'%#dyGF'F'" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "7.  \+
" }{XPPEDIT 18 0 "theta*dr+(3*r-theta-1)*d theta=0" "/,&*&%&thetaG\"\"
\"%#drGF&F&*(,(*&\"\"$F&%\"rGF&F&F%!\"\"\"\"\"F-F&%\"dGF&F%F&F&\"\"!" 
}{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 3 "21." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "i21:=\{(
1/x+2*y(x)^2*x) + (2*y(x)*x^2-cos(y(x)))*diff(y(x),x)=0, y(1)=Pi\};" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(i21,y(x));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "So Maple can't do it!  However, it
 is exact.  A potential is:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
30 "F:=ln(x)+y(x)^2*x^2-sin(y(x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "diff(F,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "29.
  " }{XPPEDIT 18 0 "(y^2+2*x*y)*dx-x^2*dy=0" "/,&*&,&*$%\"yG\"\"#\"\"
\"*(\"\"#F)%\"xGF)F'F)F)F)%#dxGF)F)*&F,\"\"#%#dyGF)!\"\"\"\"!" }{TEXT 
-1 20 "  is not exact, but " }{XPPEDIT 18 0 "y^(-2) " ")%\"yG,$\"\"#!
\"\"" }{TEXT -1 26 " is an integrating factor." }}{PARA 0 "" 0 "" 
{TEXT -1 48 "Solve the new equation.  Are any solutions lost?" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "d29:=y(x)^2+2*x*y(x)-x^2*dif
f(y(x),x)=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(d29,
y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "d29t:=d29*(y(x)^(
-2));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "dsolve(d29t,y(x));
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "12 0 0" 0 }
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