# SECTION 3.2# Example 1de := diff(x(t),t) = .6 - 3*x(t)/500;

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dsolve({de,x(0)=0});

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x := rhs(%);

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conc := x/1000.;

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solve(conc = .05,t);

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Limit(x,t=infinity);

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value(%);

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# Example 2x := 'x';

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de := diff(x(t),t) = .6 - 5*x(t)/(1000+t);

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dsolve({de,x(0)=0});

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x := rhs(%);

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conc := x/(1000.+t);

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Limit(conc,t=infinity);

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value(%);

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# Alternative solution using an integrating factor:x := 'x';

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de1 := diff(x(t),t) + 5*x(t)/(1000+t) = .6;

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P := 5/(1000.+t);

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Int(P,t);

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value(%);

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mu := exp(%);

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simplify(%);

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mu := %;

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de2 := mu*de1;

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#Check that LHS of de2 is the derivative of mu*x(t):diff(mu*x(t),t) - lhs(de2);

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simplify(%);

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# Solve de2 by integrating both sides:Int(rhs(de2),t);

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value(%);

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eq := mu*x = % + c;

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subs({t=0,x=0},eq);

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solve(%,c);

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subs(c=%,eq);

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sol := x = rhs(%)/(1000.+t)^5;

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# This result is readily seen to be equivalent to the dsolve solution.# Example 3sol := p = 3.93*exp(k*t);

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subs({t=100,p=62.98},sol);

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solve(%,k);

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subs(k=%,sol);

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# Example 4de := diff(p(t),t) = -A*p(t)*(p(t)-p1);

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dsolve({de,p(0)=p0});

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subs(p0 = 3.93,%);

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sol := p = rhs(%);;

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subs({t=50,p=17.07},sol);

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eq1 := %;

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subs({t=100,p=62.98},sol);

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eq2 := %;

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solve({eq1,eq2},{p1,A});

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subs(%,sol);

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