AS/A2 Pure 5 Pure 6

P4 Topic 6: Second Order Differential Equations
Complementary function 2
Second order differential equations of this form:.
are solved by use of the auxiliary quadratic equation: am²+bm+c=0. The solution is called the complementary function. The type of complementary function depends on the nature of the roots of the auxiliary equation, ie., on the discriminant b²-4ac. The following display shows examples where the discriminant is negative.

Summary When b²-4ac>0, the complementary function is of the form y = Aeax + Bebx. When b²-4ac=0, the complementary function is of the form y = eax(A + Bx). When b²-4ac<0, the complementary function is of the form y = Aepxcos(qx+q) or y = epx(Bcos qx+Csin qx). This page uses HotEqn.