# SECTION 9.4# Example 1with(linalg);

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x1 := [exp(t),0,exp(t)];

NiM+JSN4MUc3JS0lJGV4cEc2IyUidEciIiFGJg==

x2 := [3*exp(t),0,3*exp(t)];

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x3 := [t,1,0];

NiM+JSN4M0c3JSUidEciIiIiIiE=

c1*x1+c2*x2+c3*x3;

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subs({c1=3,c2=-1,c3=0},%);

NiM3JSIiIUYkRiQ=

# Example 2A := matrix([[1,1,1],[0,1,2],[1,-1,1]]); # Coefficient matrix of (4), Page 526

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det(A);

NiMiIiU=

# Therefore system (4) has only the trivial solution.# Example 3x1 := [exp(2*t),exp(2*t),exp(2*t)];

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x2 := [-exp(-t),0,exp(-t)];

NiM+JSN4Mkc3JSwkLSUkZXhwRzYjLCQlInRHISIiRiwiIiFGJw==

x3 := [0,exp(-t),-exp(-t)];

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XT := [ x1, x2, x3];

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evalm(XT);

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XT is the transpose of Xtranspose(%);

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X := %;

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A := matrix([[0,1,1],[1,0,1],[1,1,0]]);

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det(X);

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simplify(%);

NiMhIiQ=

# This is the Wronskian of {x1,x2,x3}. # We next show dX/dt = AX

diff(evalm(X),t);

Error, please use map to differentiate tables/arrays

?mapmap(diff,X,t);

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evalm(A &* X);;

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# Therefore dX/dt = AX