{VERSION 2 3 "SUN SPARC SOLARIS" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "p. 388, 35, 36, 37.  First
 lets see if dsolve can do them without help." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 67 "i35:=\{diff(y(t),t,t)+3*t*diff(y(t),t)-6*y(t)=1,
 y(0)=0, D(y)(0)=0\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "ds
olve(i35,y(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "i36:=\{t
*diff(y(t),t,t)-t*diff(y(t),t)+y(t)=2, y(0)=2, D(y)(0)=-1\};" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(i36,y(t));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "i37:=\{t*diff(y(t),t,t)-2*di
ff(y(t),t)+t*y(t)=0, y(0)=1, D(y)(0)=3\};" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 17 "dsolve(i37,y(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 71 "So you need a better tool here.  Notice that the Laplace transf
orm of  " }{XPPEDIT 18 0 "t*f(t)" "*&%\"tG\"\"\"-%\"fG6#F#F$" }{TEXT 
-1 6 "  is  " }{XPPEDIT 18 0 "-diff(F(s),s)" ",$-%%diffG6$-%\"FG6#%\"s
GF)!\"\"" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(inttrans):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 20 "laplace(t*f(t),t,s);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 25 "dsolve(i37,y(t),laplace);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 29 "!  It can do it!  Wonder how?" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "alias(Y(s)=
laplace(y(t),t,s)); newde:=laplace(t*diff(y(t),t,t)-2*diff(y(t),t)+t*y
(t),t,s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "fixinit:=subs(
\{y(0)=1, D(y)(0)=3\}, newde);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 21 "dsolve(fixinit,Y(s));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 30 "fixY:=subs(Y(s)=G(s),fixinit);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "dsolve(fixY,G(s));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "invlaplace(\",s,t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 47 "Now find _C1 from the original init conditions." }}}}{MARK "18 \+
0 0" 47 }{VIEWOPTS 1 1 0 2 1 1805 }