Is the required solution. ex solve [d+ + (m +n )d +m'n*]y =cos(m +n)cos(m-n) 2 sol the auxiliary equation is m4+ (m2 + n2)m2 + mn2 = 0 (m2+m )(m2 + n?) = 0 m =

is the required solution. Ex Solve [D+ + (m +n )D +m'n*]y =cos(m +n)cos(m-n) 2 Sol The auxiliary equation is m4+ (m2 + n2)m2 + mn2 = 0 (m2+m )(m2 + n?) = 0 m = t im, t in So, CF = C, COS mx + C, Sin mx+ C, COs nx + C, Sin nx m-n m+Dxcos2 1 COs Pl= (D +m(D +n) 2 and 2 (COS mxX+COS nx) 2(D +m )(D +n) 1x sin mx X Sin nX 2 2m(n-m) 2n(m-n) X - sin mx--Sin nx n 4(n-m)Lm sin mx-sin nx n y= C, Cos mx +C, Sin mX +Cg COS nx +C Sin nx t 4(n-m)Lm