D-3-2D-2-9D-18-y-6cos3x- Tinku Tara June 4, 2023 Differential Equation 0 Comments FacebookTweetPin Question Number 56580 by subhankar10 last updated on 18/Mar/19 (D3−2D2+9D−18)y=6cos3x Answered by tanmay.chaudhury50@gmail.com last updated on 19/Mar/19 lety=emxbeasolutionDy=memxD2y=m2emx..socomplimentaryfunctionm3emx−2m2emx+9memx−18emx=0emx(m3−2m2+9m−18)=0emx≠0m3−2m2+9m−18=0m2(n−2)+9(m−2)=0(m−2)(m2+9)=0m=2and±3iC.FC1e2x+C2ei3x+C3e−i3xParticularintregaly=6cos3xD3−2D2+9D−18=6×cos3xD2(D−2)+9(D−2)=6×cos3x(D−2)(D2+9)=6×(D+2)cos3x(D2−4)(D2+9)=6(−32−4)×−3sin3x+2cos3xD2+9=−613×−3sin3x+2cos3xD2+9=613×(3sin3x−2cos3x)D2+9=613×rsin(3x−θ)D2+9[r=32+22=13tanθ=23]p=613×cos(3x−θ)D2+9q=613×sin(3x−θ)D2+9p+iq=613×ei(3x−θ)D2+9p+iq=613×e−iθ×ei×3xD2+9p+iq=613×e−iθ×ei3x(D+i3)(D−i3)p+iq=613×(cosθ−isinθ)×ei3x(i3+i3)(D+i3−i3)×1=613×(313−i×213)×(cos3x+isin3x)6i×x=113×3i+2i2×(xcos3x+ixsin3x)=−113(i3xcos3x−3xsin3x+2xcos3x+i2xsin3x)=−113{(2xcos3x−3xsin3x)+i(3xcos3x+2xsin3x)}=−x13(2cos3x−3sin3x)+−ix13(3cos3x+2sin3x)nowouranswerisrelatedtocomplexpartsoanswerisParticularintregalis=−x13(3cos3x+2sin3x)socomplteansweris=C.F+P.Iy=C1e2x+C2ei3x+C3e−i3x+−x13(3cos3x+2sin3x) Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-56578Next Next post: tanA-1-cotA-cotA-1-tanA-secA-cosecA-1-Please-prove-it-for-me- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.