Question

A nonhomogeneous second-order linear equation and a complementary function ye are given below. Use the method of variation of parameters to find a particular solution of the given differential equation. Before applying the method of variation of parameters, divide the equation by its leading coefficient x2 to rewrite it in the standard form, y" + P(x)y'+Q(x)y = f(x) x2y"xy'y Inx; y c1 cos (In x) + c2 sin (In x) The particular solution is yo (x)

Answer 1

x°y” + x 9'+ y + Ép 4 => y" + y! + terys love ice. y " + pln) y't Plu). y = feu), while fow) - Pena Ye : 4 ans 1 enx) + ez sin ( ena) given. so, Y, CH) = cos (anx), Y26) = sin( enx). wronskiun (W) = 1 yn y l l cas (enn) sin(ina) l y a 1 . | - sin(ano) CD ( 214 ) - [ logº ( 10x) + sin(ne) ? So, by variation of parameter method Yp (n) = -4, 5 pz fel du +421 fra de - - Colemas con los at bilens 2 - colson). ann. singarin) sa t cincinum). S au ca, con un == 60 (dom). J a sina fet sig som ſa cont de protein - - 60 (me{ z line 01 - for segu] is as asenne fering 1 =) dz

yo(u) = enn. lee. ки - (име) ми - (+) и P (км) ту: кит - [hur) wat (««дом - ve] »ку чу - [ «умя (os) •r -] (sv) ш. . [ + мя. | («д», - Lost tot-| wr)) . .