CAPE Pure Mathematics Unit 2 · May/June 2015 · 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 \lambda(x) dx} = \int Q(x) e^{\int \lambda(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)