solve-y-y-sin-x- Tinku Tara June 4, 2023 Differential Equation 0 Comments FacebookTweetPin Question Number 100344 by bemath last updated on 26/Jun/20 solvey″+y=sinx Answered by bobhans last updated on 26/Jun/20 homogenoussolutionη2+1=0⇒η=±iyh=Asinx+Bcosxparticularsolutionyp=x(Asinx+Bcosx)yp′=Asinx+Bcosx+x(Acosx−Bsinx)yp″=2Acosx−2Bsinx+x(−Asinx−Bcosx)A=0∧B=12yp=12xcosxGenerallsolutionyg=Asinx+Bcosx+12xcosx Answered by mathmax by abdo last updated on 26/Jun/20 y″+y=sinx(he)→r2+1=0⇒r=+−i⇒yh=aeix+be−ix=αcosx+βsinx=αu1+βu2W(u1,u2)=|cosxsinx−sinxcosx|=1W1=|0sinxsinxcosx|=−sin2xW2=|cosx0−sinxsinx|=cosxsinxv1=∫w1wdx=−∫sin2x1dx=−∫1−cos(2x)2=−x2+14sin(2x)v2=∫w2wdx=∫cosxsinxdx=12∫sin(2x)dx=−14cos(2x)⇒yp=u1v1+u2v2=cosx(−x2+14sin(2x))+sinx(−14cos(2x))=−x2cosx+14cosxsin(2x)−14sinxcos(2x)=−x2cosx+12cos2xsinx−14sinx(2cos2x−1)=−x2cosx+14sinxthegeneralsolutionisy=yh+yp=αcosx+βsinx−x2cosx+14sinx Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: l-x-0-im-f-x-1-1-x-f-1-f-1-help-me-Next Next post: x-y-y-x-3-2-x-y-xy-9- Leave a Reply Cancel replyYour email address will not be published.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.