Q) Solve the IBUPL PDE: U=Uxx xdx, 4150cher ucoblo لا uc, bl=csbou (HE BEST IC! Urgels QCX) ; X€ [01] By superposition m

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Q) Solve the IBUPL PDE: U=Uxx xdx, 4150cher ucoblo لا uc, bl=csbou (HE BEST IC! Urgels QCX) ; X€ [01] By superposition method. Note. Els you can Solo Cal directly by using . Sulu Sinite, sine transform (lesson 25)
lesson(261 Superposition (The Backbone of linear system) o @ This technique is used to scive linear IBUPS. (c.e. The PPE and Bes should be linear) The procedure: break the IBup into subproblems, thes, Salve each subpart individually, and their add the results of each part. PDF! Ex-i consider The IBUPS u = Uxx + f(x,t; aste (1</ Best wat oo too t=0 fc:UX, 01 - P(X); Osxsd To solve cih, break the IBUPL into two parts: You candt use separation of variables to ) Snce the pos is nonhomog. solvec) و ) land مدار IBUP PDE: Ut=C2x + $(x, ki Be's fula,t=0 otro ulb, b=0 PDG. U = Uxx Besluca, bl=0 Tulb,tl=0 , Icila,o=941 feu Best میرا (2) IC: Ucx,al=0 If U, is the sala. of (a) and U2 is the u Solution of (3), then U=u, tuz is Solu- for (I). Called superposition principle
Solve the Ievip - 9 PdE: Ui_ Uxx + f(xt) ,0 5x11 tro B. 25. Julesto (lt)=0 I.C-U (x,c) = P(x) x 6 [at] By super position Backbone linear system you can solve by by directly by using finite sine transform