# SECTION 5.1de1 := diff(x(t),t) = y(t)/12 - x(t)/3;

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de2 := diff(y(t),t) = x(t)/3 - y(t)/3;

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solve(de2,x(t));

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subs(x(t)=%,de1);

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expand(%);

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denew := lhs(%)-rhs(%)=0;

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# Solve by the methods of Section 4.2:P := 3*r^2+2*r+1/4;

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rsol := solve(P=0,r);

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r1 := rsol[1]; r2 := rsol[2];

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y1 := exp(r1*t); y2 := exp(r2*t);

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ysol := c1*y1+c2*y2;

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xsol := 3*diff(ysol,t)+ysol;

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subs(t=0,xsol);

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eq1 := % = x0;

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subs(t=0,ysol);

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eq2 := % = y0;

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solve({eq1,eq2},{c1,c2});

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subs(%,{xsol,ysol});

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