# SECTION 4.6# Example 1# de := diff(y(t),t,t) + y(t) = tan(t);y1 := cos(t); y2 := sin(t);

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eq1 := y1*v1p + y2*v2p = 0;

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eq2 := diff(y1,t)*v1p + diff(y2,t)*v2p = tan(t);

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v1p := 'v1p'; v2p := 'v2p';

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sol := solve({eq1,eq2},{v1p,v2p});

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v1p := rhs(sol[1]);

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v2p := rhs(sol[2]);

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Int(v1p,t);

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value(%);

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v1 := % + C1;

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v2 := int(v2p,t) + C2;

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y := v1*y1 + v2*y2;

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expand(%);

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# Example 2y := 'y';

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de := diff(y(t),t,t) + y(t) = tan(t) + 3*t -1;

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dsolve(de);

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