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(2 marks) Find a particular solution, yp(z), of the non-homogeneous differential equation d² 23 (2) +2(3 (2)) + y(x) = 28 e³z₁ +Bze is the general solution of the corresponding given that y(x) = Ae¯ homogeneous ODE. The form of yp (2) that you would try is O yp = ax + b Up = ae³z Up = az²e-z О yp = axe -2 O up = ae Ⓒup = aze³z Enter your answer in Maple syntax only the function defining up (x) in the box below. For example, if your particular solution is yp (x) = 3x+4, enter 3*x+4 in the box. yp (z) = In
(3 marks) The general solution of the homogeneous differential equation d² dz2(z)-10- 10 —y (x) + 25 y (x) = 0 is given by where a = 5 axe7x 5 and A and B are arbitrary constants. uh ae7x az²e7x (az + b)e7z = Aeªz a) What form would you take as your guess? Let us now find a particular solution to the non-homogeneous differential equation d² zy (z) — 10 —y (z) + 25 y (z) = 5e7ª. dz2 up = + Bxeba and b b) Enter your particular solution up (of the above form, evaluating a and/or b) in the box below.