# SECTION 3.3# Example 1de := diff(T(t),t) = K*(M0-T(t));

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dsolve({de,T(t0)=T0});

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sol := %;

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# Alternative solution using an integrating factor:de1 := diff(T(t),t) + K*T(t) = K*M0;

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P := K;

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mu := exp(int(P,t));

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de2 := mu*de1;

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# Check that LHS = derivative of mu*T(t):diff(mu*T(t),t) - lhs(de2);

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simplify(%);

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# Integrate both sides of de2:Int(rhs(de2),t);

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value(%);

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mu*T = %+C;

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solve(%,T);

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simplify(%);

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expand(%);

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sol := T = %;

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subs({t=t0,T=T0},sol);

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solve(%,C);

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subs(C=%,sol);

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simplify(%);

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# Example 2 de1 := diff(T(t),t) + K*T(t) = K*(M0-B*cos(omega*t))+H0;

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dsolve(de1);

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dsolve({de1,T(0)=T0});

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# Alternative solution using an integrating factor:

sol := 'sol';

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mu := exp(int(K,t));

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de2 := mu*de1;

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Int(rhs(de2),t);

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value(%);

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sol := mu*T = % + C;

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subs({t=0,T=T0},%);

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solve(%,C);

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subs(C=%,sol);

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T = rhs(%)/mu;

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# Example 2de := diff(T(t),t) = K*(M-T(t))+H+Ku*(Td-T(t));

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subs({M=M0-B*cos(omega*t),H=H0},de);

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subs(K=K1-Ku,%);

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de := %;

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dsolve(de);

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dsolve({de,T(0)=T0});

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