Question

Consider the following nonhomogeneous linear differential equation ay 6) + by(s) + cy!4) + dy'"' + ky'' + my' + ny=3x²3x - 7cos +1 where coefficients a, b, c, d, k, m, n are constant. Assume that the general solution of the associated homogeneous linear differential equation is YAEC,+Ce**+ c xe** + c.xe3* + ecos What is the correct form of the particular solution y of given nonhomogeneous linear differential equation? Yanitiniz: o Yo=Ax*e** + Ex + F **+Cxcos() +oxsin()+Ex+F O V=Ax*e**+Bx*e*+ csin(t) + Dcos() +Ex O Y = Ax*e*+Bx*e**+cxe** +Dxcos() +Exsin(my)+fx OY=ax*e**+B**e**+cx*e**+Dcos(1) + Esin($)+F O None of the above Yaniti temizle

Answer 1

3x 37 3x املہ "te 't C4 we have given the differential eqreation, ago) +by's) + eyA + d y" + Ky" + my't Eny - 323% - 7 Con (%) + 1 Also we have given the general solution 06 the corresponding homogeneous equation of =c, to + Cg Cos (3) + Co Sin (3) -02 From (22) observe the following (1) auxiliary equation of the home of . Also Re H.S. of cos (3) which is in (22) atso present R.H.S. of (i) can take the particular solution. zwe is a briple root of the ogeneous equation 32 oceurs en (22) en So zwe ad, 3x Az A4 25e 30 = (,+ A2x + 433e?) 44233x + x CD Cota + Esin ) + FX 43x + A,A4X x² e 3 x + Ox Cos (3) + £x Sin () + Fr. yo Axe3X + Bx432 + x3e + DX COD ($) + Ex sin ( 3 ) + Fx. + AZAM x 3x