Past exam of the mathematics course of the University of Cambridge / 2010 / ia / Paper 2 / 7A / c / Solution

At $\lambda =-1$ the $v_{-}$ forcing vanishes and the $v_{+}$ forcing coefficient is $-2$. The initial vector decomposes asThus $A=1/2$, $B=0$, $C=-1/2$ in part (b), and the requested solution isEquivalently,These expressions have the required initial values and solve all three linear ordinary differential equations.