# SECTION 4.1# Example 1de := m*diff(y(t),t,t) + k*y(t) = 0;

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dsolve(de);

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# Example 2de := m*diff(y(t),t,t) + b*diff(y(t),t) + k*y(t) = 0;

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subs({m=1,b=6,k=25},de);

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de2 := %;

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subs(y(t) = exp(-3*t)*cos(4*t),de2);

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expand(%);

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# Example 3de;

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subs({m=1,b=10,k=25},de);

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de3 := %;

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subs(y(t) = exp(-5*t),de3);

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expand(%);

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# Example 4subs({m=1,b=1,k=25},de);

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de4 := lhs(%) = sin(Omega*t);

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subs(y(t) = A*cos(Omega*t)+B*sin(Omega*t),de4);

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eq := expand(%);

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eq1 := -Omega^2*B -Omega*A +25*B = 1;

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eq2 := -Omega^2*A +Omega*B +25*A = 0;

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

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# Alternative way to get eq1 and eq2:subs(t=pi/2/Omega,eq);

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simplify(%);

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subs({cos(pi/2)=0,sin(pi/2)=1},%);

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subs(t=0,eq);

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simplify(%);

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