CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 1 · Question Q42

If the auxiliary equation for a homogeneous second order differential equation with real, constant coefficients is given by \lambda^2 + 6\lambda + 50 = 0, then the general solution of the differential equation may be given by

1. (A)y = e^{\lambda x}(A + Bx)
2. (B)y e^{\int P(x)dx} = \int Q(x)e^{\int P(x)dx}dx + C
3. (C)y = A e^{\lambda_1 x} + B e^{\lambda_2 x}
4. (D)y = e^{\alpha x}(A \cos \beta x + B \sin \beta x)