{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 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 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "P\370\355klad 7" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "Naleznete partiku larni reseni rovnice " }{TEXT 256 33 "y''' + 2y'' + 4y' + 8y = 32cos2x " }{TEXT -1 23 "pro pocatecni podminky " }{TEXT 257 25 "y(0)=2, y'(0) =6, y''(0)=0" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "rovnice3:= diff(y(x),x$3)+2*diff(y(x),x$2)+4*diff(y(x),x)+8*y(x)=32*cos(2*x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)rovnice3G/,*-%%diffG6$-%\"yG6#%\"xG -%\"$G6$F-\"\"$\"\"\"*&\"\"#F2-F(6$F*-F/6$F-F4F2F2*&\"\"%F2-F(6$F*F-F2 F2*&\"\")F2F*F2F2,$-%$cosG6#,$F-F4\"#K" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "podminky:=[[0,2],[0,6],[0,0]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)podminkyG7%7$\"\"!\"\"#7$F'\"\"'7$F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Pro informaci vypocteme koreny charakter isticke rovnice a vyjadrime obecne reseni prislusne homogenni rovnice. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "read \"difproc.m\": so lve(char(lhs(rovnice3)=0,y(x)),lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%!\"#^#\"\"#^#F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "ho m(lhs(rovnice3)=0,y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#% \"xG,(*&&%\"cG6#\"\"\"F--%$expG6#,$F'!\"#F-F-*&&F+6#\"\"#F--%$sinG6#,$ F'F6F-F-*&&F+6#\"\"$F--%$cosGF9F-F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Pro nalezeni obecneho reseni nehomogenni rovnice pouzijeme proc eduru " }{TEXT 258 8 "varconst" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 36 "ob_reseni:=varconst(rovnice3,y(x)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*ob_reseniG/-%\"yG6#%\"xG,0*&&%\"cG6#\"\" \"F/-%$expG6#,$F)!\"#F/F/*&&F-6#\"\"#F/-%$sinG6#,$F)F8F/F/*&&F-6#\"\"$ F/-%$cosGF;F/F/*&F8F/FAF/F/F9F/*(F8F/F9F/F)F/F/*(F8F/FAF/F)F/!\"\"" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 "Do obecneho reseni a jeho prvni a druhe derivace postupne dosadime zadane pocatecni podminky." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "dosazeni1:=2=subs(x=0,rhs(ob _reseni));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*dosazeni1G/\"\"#,,*&& %\"cG6#\"\"\"F,-%$expG6#\"\"!F,F,*&&F*6#F&F,-%$sinGF/F,F,*&&F*6#\"\"$F ,-%$cosGF/F,F,F4F,*&F&F,F:F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "dosazeni2:=6=subs(x=0,diff(rhs(ob_reseni),x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*dosazeni2G/\"\"',**&&%\"cG6#\"\"\"F,-%$expG6#\" \"!F,!\"#*(\"\"#F,&F*6#F3F,-%$cosGF/F,F,*(F3F,&F*6#\"\"$F,-%$sinGF/F,! \"\"*&F3F,F" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "dosazen i3:=0=subs(x=0,diff(rhs(ob_reseni),x$2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*dosazeni3G/\"\"!,**&&%\"cG6#\"\"\"F,-%$expG6#F&F,\" \"%*(F0F,&F*6#\"\"#F,-%$sinGF/F,!\"\"*(F0F,&F*6#\"\"$F,-%$cosGF/F,F7*& F0F,F5F,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "Resenim soustavy do staneme hodnoty neznamych konstant " }{XPPEDIT 18 0 "c[1];" "6#&%\"cG6 #\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "c[2];" "6#&%\"cG6#\"\"#" } {TEXT -1 2 ", " }{XPPEDIT 18 0 "c[3];" "6#&%\"cG6#\"\"$" }{TEXT -1 1 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "konstanty:=solve(\{dos azeni1,dosazeni2,dosazeni3\},\{c[1],c[2],c[3]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*konstantyG<%/&%\"cG6#\"\"\"\"\"!/&F(6#\"\"#\"\"$/&F( 6#F0F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "Dosazenim do obecneho \+ reseni dostaneme partikularni reseni vyhovujici zadanym pocatecnim pod minkam. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "part_reseni:= y[p](x)=subs(konstanty,rhs(ob_reseni));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,part_reseniG/-&%\"yG6#%\"pG6#%\"xG,*-%$sinG6#,$F,\"\"#\"\"%*& F2\"\"\"-%$cosGF0F5F5*(F2F5F.F5F,F5F5*(F2F5F,F5F6F5!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 " Partikularni reseni muzeme hledat take p omoci procedury " }{TEXT 260 4 "part" }{TEXT -1 32 ", nebo primo pouzi tim procedury " }{TEXT 259 8 "varconst" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "part(ob_reseni,podminky);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,*-%$sinG6#,$F'\"\"#\"\"%*&F- \"\"\"-%$cosGF+F0F0*(F-F0F)F0F'F0F0*(F-F0F1F0F'F0!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "varconst(rovnice3,y(x),podminky);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,*-%$sinG6#,$F'\"\"#\" \"%*&F-\"\"\"-%$cosGF+F0F0*(F-F0F)F0F'F0F0*(F-F0F1F0F'F0!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "Dosazenim overime, zda toto reseni vyhovuje zadane rovnici." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "subs(y(x)=rhs(part_reseni),rovnice3): simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,$-%$cosG6#,$%\"xG\"\"#\"#KF$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Zobrazime graf nalezeneho partikularniho reseni. 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