Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 2 / 15 / b / iii

The equation $u=v^{\prime }$ fixes $u$ from the same two constants:Indeed $u^{\prime }=4A{e}^{2t}+4B{e}^{-2t}=4v+2$, so both original equations hold. No further independent integration constant is available in this two-dimensional linear system of ordinary differential equations.