Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability (resit) / 5 / a / iii

Put $a=\pi /2$. Substituting $x=-a$ and $x=a$ into part (ii), using $\cos (\pi /4)=\sin (\pi /4)=1/\sqrt{2}$, givesThus $A-B=\sqrt{2}(1+e^{-a})$ and $A+B=\sqrt{2}(1-e^a)$. Solving these two linear equations givesConsequently the solution of the boundary value problem isThe two independent boundary conditions determine $A,B$ uniquely.