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3.0, solution ‘ Paper 5, Let x = e”, , a 2 log x, Then x7 = Dy where D = £., 2 & =D(D-1)y, the given differential equation becomes, , [DD -1)-3D]y=er+1, , 2, (0 - 4D) ye 41, The auxiliary equation is m - 4m =0, , , , m = 0,4., The complementary function is, y=A + Be*, The Particular Integral is, Pl= ot 1, p- D*~ 4D, =e aa, +*p@o-4, ee, ~ 3 4°D°, ate i, =3 a", iat, +, The complete solution is y = =A+Be"-3¢ - 4, yaa + Bx’ - Ej loex, Example 4 ,, ww), dy _ phd 4 B =P loge. (, solve 75 oe dx, dh :, Solution 4 . © wi Shak, =V. n =, Let v. Then 2 x a, becomes, , . the given DE