(1305U40-1) 6 © WJEC CBAC Ltd. 11. Evaluate the integrals (a) [5] (b) [9] 12. Find the general solution of the equation cos4θ  + cos2θ = cosθ. [6] 13. Two species of insects, X and Y, co-exist on an island. The populations of the species at time t years are x and y respectively, where x and y are measured in millions. The situation can be modelled by the differential equations (a) (i) Show that d2x dt2 −9 dx dt + 8x = 0 . (ii) Find the general solution for x in terms of t. [7] (b) Find the corresponding general solution for y. [4] (c) When t = 0, dx dt = 5 and the population of species Y  is 4 times the population of species X. Find the particular solution for x in terms of t. [6] END OF PAPER e2x −2 0∫ sinhxdx,    3 2 5 d 1 9 x x x    . dx dt = 3x +10y, dy dt = x + 6y . 3 2 (1305U40-1) 7 © WJEC CBAC Ltd. BLANK PAGE