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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" 
{TEXT -1 80 "Warning, the protected names norm and trace have been red
efined and unprotected\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Teht
\344v\344 1:" }{MPLTEXT 1 0 166 "A:=linalg[matrix](3,3,[x^(alpha),x^(b
eta),x^(gamma),diff(x^(alpha),x),diff(x^(beta),x),diff(x^(gamma),x),di
ff(x^(alpha),x,x),diff(x^(beta),x,x),diff(x^(gamma),x,x)]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%)%\"xG%&alphaG)F+%%bet
aG)F+%&gammaG7%*&*&F*\"\"\"F,F4F4F+!\"\"*&*&F-F4F.F4F4F+F5*&*&F/F4F0F4
F4F+F57%,&*&*&F*F4)F,\"\"#F4F4*$)F+F?F4F5F4*&*&F*F4F,F4F4*$FAF4F5F5,&*
&*&F-F4)F.F?F4F4*$FAF4F5F4*&*&F-F4F.F4F4*$FAF4F5F5,&*&*&F/F4)F0F?F4F4*
$FAF4F5F4*&*&F/F4F0F4F4*$FAF4F5F5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "simplify(A,symbolic);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%'matrixG6#7%7%)%\"xG%&alphaG)F)%%betaG)F)%&gammaG7%*&)F),&F*\"
\"\"F3!\"\"F3F*F3*&)F),&F,F3F3F4F3F,F3*&)F),&F.F3F3F4F3F.F37%,&*&)F),&
F*F3\"\"#F4F3)F*F@F3F3*&F>F3F*F3F4,&*&)F),&F,F3F@F4F3)F,F@F3F3*&FEF3F,
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0 "" {MPLTEXT 1 0 15 "factor(det(A));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#*&*.)%\"xG%&alphaG\"\"\")F&%%betaGF()F&%&gammaGF(,&F*F(F'!\"\"F(,&F
'F.F,F(F(,&F,F(F*F.F(F(*$)F&\"\"$F(F." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 22 "Teht\344v\344\344n 2. liittyen:" }{MPLTEXT 1 0 193 "B:=li
nalg[matrix](3,3,[exp(alpha*x),exp(beta*x),exp(gamma*x),diff(exp(alpha
*x),x),diff(exp(beta*x),x),diff(exp(gamma*x),x),diff(exp(alpha*x),x,x)
,diff(exp(beta*x),x,x),diff(exp(gamma*x),x,x)]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"BG-%'matrixG6#7%7%-%$expG6#*&%&alphaG\"\"\"%\"xGF/-
F+6#*&%%betaGF/F0F/-F+6#*&%&gammaGF/F0F/7%*&F.F/F*F/*&F4F/F1F/*&F8F/F5
F/7%*&)F.\"\"#F/F*F/*&)F4F@F/F1F/*&)F8F@F/F5F/" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "factor(det(B));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*.-%$expG6#*&%&gammaG\"\"\"%\"xGF)F)-F%6#*&%&alphaGF)F*F)F)-F%6#
*&%%betaGF)F*F)F),&F2F)F.!\"\"F),&F.F4F(F)F),&F(F)F2F4F)" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 10 "Teht\344v\344 3:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{MPLTEXT 1 0 45 "dy3:=(1-x^2)*D(D(y))(x)-2*x*D(y)(x)+2*
y(x)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dy3G/,(*&,&\"\"\"F)*$)%
\"xG\"\"#F)!\"\"F)---%#@@G6$%\"DGF-6#%\"yG6#F,F)F)*(F-F)F,F)--F4F5F7F)
F.*&F-F)-F6F7F)F)\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "d
solve(dy3,y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,&*&
%$_C1G\"\"\"F'F+F+*&%$_C2GF+,&*&F'F+-%#lnG6#,$*&,&F'F+F+F+F+,&F'F+F+!
\"\"F7F7F+#F+\"\"#F+F7F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
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