Variation of Parameters
Replace the constants in the homogeneous solution c1*y1 + c2*y2 with functions u1(t), u2(t) and solve the resulting system, giving u1' = -y2*g/W and u2' = y1*g/W where W is the Wronskian. Unlike undetermined coefficients it handles arbitrary forcing functions and variable coefficients, at the cost of two integrals that may lack closed forms.
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Replace the constants in the homogeneous solution c1*y1 + c2*y2 with functions u1(t), u2(t) and solve the resulting system, giving u1' = -y2*g/W and u2' = y1*g/W where W is the Wronskian. Unlike undetermined coefficients it handles arbitrary forcing functions and variable coefficients, at the cost of two integrals that may lack closed forms.
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