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{SECT 0 {EXCHG {PARA 18 "" 0 "top_s11_1" {TEXT -1 24 "11.1  Explicit S
olutions" }}{PARA 19 "" 0 "" {TEXT -1 25 "Art Belmonte, Summer 1996" }
}{PARA 0 "" 0 "" {TEXT -1 64 "These are the shaded gray examples which
 appear in Section 11.1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 
"restart; eq1:=diff(y(t), t) + 5*y(t) = 2*t;\ndsolve(eq1, y(t));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/,&-%%diffG6$-%\"yG6#%\"tGF-\"
\"\"F*\"\"&,$F-\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG
,(F'#\"\"#\"\"&#!\"#\"#D\"\"\"*&-%$expG6#,$F'!\"&F/%$_C1GF/F/" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "dsolve(\{eq1, y(1)=2\}, y(t)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,(F'#\"\"#\"\"&#!
\"#\"#D\"\"\"*&-%$expG6#,$F'!\"&F/-F26#F5!\"\"#\"#UF." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "y:=evaln(y); eq2:=diff(y(t), t$2) +
 6*diff(y(t), t) - 7*y(t) = 1;\ndsolve(eq2, y(t));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"yGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/,
(-%%diffG6$-F(6$-%\"yG6#%\"tGF/F/\"\"\"F*\"\"'F,!\"(F0" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,(#!\"\"\"\"(\"\"\"*&%$_C1GF,-%$expG
F&F,F,*&%$_C2GF,-F06#,$F'!\"(F,F," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 39 "dsolve(\{eq2, y(1)=3, D(y)(1)=2\}, y(t));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG,(#!\"\"\"\"(\"\"\"*&-%$expG6#
F,F*-F/F&F,\"\"$*&F.F+-F/6#,$F'!\"(F,#F,F+" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{MARK "5 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }