use-power-series-solution-method-to-solve-the-ODE-y-xy-0- Tinku Tara June 4, 2023 Differentiation 0 Comments FacebookTweetPin Question Number 99646 by 24224 Opiyo Kamuki last updated on 22/Jun/20 usepowerseriessolutionmethodtosolvetheODEy″−xy=0 Answered by MWSuSon last updated on 22/Jun/20 ∑∞k=2k(k−1)akxk−2−x∑∞k=0akxk=0∑∞k=0(k+1)(k+2)ak+2xk−∑∞k=0akxk+1=0∑∞k=0(k+1)(k+2)ak+2xk−∑∞k=1ak−1xk=02a2+∑∞k=1[(k+2)(k+1)ak+2−ak−1]xk=0a2=0recurrencerelationfork⩾1ak+2=ak−1(k+2)(k+1)inputvaluesfork=1,2,3,4,5,…andfindakintermsofa0anda1 Answered by mathmax by abdo last updated on 22/Jun/20 y=∑n=0∞anxn⇒y′=∑n=1∞nanxn−1⇒y″=∑n=2∞n(n−1)anxn−2=∑n=0∞(n+2)(n+1)an+2xne⇒∑n=0∞(n+1)(n+2)an+2xn−∑n=0∞anxn+1=0⇒∑n=0∞(n+1)(n+2)an+2xn−∑n=1∞an−1xn=0⇒2a2+∑n=1∞{(n+1)(n+2)an+2−an−1}xn=0⇒a2=0andan+2=an−1(n+1)(n+2)(n⩾1)⇒a3=a02.3a4=a13.4,a5=a24.5,….⇒y(x)=a0+a1x+a2x2+a3x3+a4x4+…=a0+a1x+a06x3+a112x4+a220x5+… Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-34110Next Next post: Question-34114 Leave a Reply Cancel replyYour email address will not be published.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.