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 / ii / Solution

For a particular solution, try $y_p=a\sin x+b\cos x$. Substitution givesMatching coefficients requires $a-8b=1$ and $8a+b=8$, so $a=1$ and $b=0$. Adding the homogeneous solution from part (i), the general solution is