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Section “B”(Answer question 21 and any other question) [10 Marks) 21. (a) Show that the particular solution y(tr) to the second order linear ODE V" + p() +(x) = g(x) is given by ()g(0) y(r) de W(91,312) where yi and vs are basis solutions for the homogeneous equation " + P(x) + (r)y=0 [6 Mark) (b) Solve the ODE by separation of variables dy ry+ 3.r-y-3 ay - 2x + 4y - 8 der [4 Marks) (c) The differential equation dy -*+r+y de describes the shape of a plane curve C that will reflect all incoming light beams to the same point and could be a model for the mirror of a reflecting telescope, a satellite antenna, or a solar collector. Show that the substitution v=ur yields udu Vo? + 1(1 - Vu+1) 1 de