Question

Find a particular solution, yp(x), of the non-homogeneous differential equation d2 +y(x) = 6 ((x)) +9 y(x) = 6 x+2, d x2 given that yh(x) = A e3x +B x @3x is the general solution of the corresponding homogeneous ODE. The form of yp(x) that you would try is Oyp = ax + b Oyp = a 2x Oyp = ax2 3x Enter your answer in Maple syntax only the function defining yp(x) in the box below. For example, if your particular solution is yp (x) = 3 x +4, enter 3*x+4 in the box. yp(x) =

Answer 1

y"-6 y' +9 ya) = 6X +3 Pesticulay solution the right side of given Equation is a linear Hunction 7x= axtb, there fore, we will look ter a pesticule solution in the form y, Y = AXtB then Y, '= y" - 0 substituting this en the differential Equatim gives 0-6 A t 9 C AX+B) = 6xt? - A + 9 A X +9B = 2+? Tofficent with like powers of x en the right and lett side must be identical. -6A + 9B = 2 9 A = 6 =) A = 6 = 2 / So -6x + 9B = 2 :?. - 4+9B = gB= 6 = B = 45 بہایا then Postituly solution is y = کہ ای)