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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 154 "The following procedure s
olves the initial value problem x' = Ax + f(t), where A is a matrix an
d f(t) is a column vector with functions of t for enteries." }}{PARA 
0 "" 0 "" {TEXT -1 93 "The Syntax is VarParam(Matrix, Nonhomogeneous p
art as a column vector, initial value vector);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 266 "with(linalg):\nVarParam:=proc(A, f, v)\nlocal
 integrand, integral;\nintegrand:=evalm(exponential(A,-t) &* (-1*f));
\nintegral:=simplify(map(int, integrand, t=0..s));\nsimplify(evalm(exp
onential(A,s) &* (v + integral)));\nprintf(\"%s\", \"The solution is:
\");\nsubs(s=t, %);\nend:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "An e
xample follows:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "A:=array
([[4,2],[3,-1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6
#7$7$\"\"%\"\"#7$\"\"$!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
36 "f:=<<15*t*exp(-2*t),4*t*exp(-2*t)>>;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"fG-%'RTABLEG6%\")/k\")=-%'MATRIXG6#7$7#,$*(\"#:\"\"\"%\"tGF1
-%$expG6#,$*&\"\"#F1F2F1!\"\"F1F17#,$*(\"\"%F1F2F1F3F1F1%'MatrixG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "v:=<<7,3>>;" }}{PARA 11 "" 
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\"\"$%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "VarParam(
A,f,v);" }}{PARA 6 "" 1 "" {TEXT -1 16 "The solution is:" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7#,**&#\"\"\"\"\"#F+*&-%$expG6#,$*
&F,F+%\"tGF+!\"\"F+)F3F,F+F+F4*&#\"\"$\"\"(F+F.F+F+*(F,F+F3F+F.F+F+*&#
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