Question

IGNORE (i)

Problem #2: Consider the following statements. [6 marks] (i) Most of the material in Lecture Notes from Week 3 to Week 5, inclusive, can be extended or generalized to higher-order ODES. (ii) The procedure of finding series solutions to a homogeneous linear second-order ODEs could be accurately described as the method of undetermined series coefficients". (iii) The underlying idea behind the method of undetermined coefficients is a conjecture about the form of a particular solution that is motivated by the right-hand side of the equation. The method of undetermined coefficients is limited to second-order linear ODEs with constant coefficients and the right-hand side of the ODE cannot be an arbitrary function. (iv) The particular solution of the ODE y" – 6y' + 9y = 6e3x is given by yp = Cxe3x where C is an undetermined constant. (v) We must rethink what we mean by solving y"+y' - y = {co cos(x + 28) x + 1 x = 1 before trying to compute a solution defined on an interval containing x = 1. (vi) A Taylor series is a power series that gives the expansion of a function around a point a. Convergence of such series is fully understood by means of the ratio test. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True False,False,True,False,True then you would enter '1,2,2,1,2,1' into the answer box below (without the quotes).

(ii) The procedure of finding series solutions to a homogeneous linear second-order ODEs could be accurately described as the “method of undetermined series coefficients”. (iii) The underlying idea behind the method of undetermined coefficients is a conjecture about the form of a particular solution that is motivated by the right-hand side of the equation. The method of undetermined coefficients is limited to second-order linear ODEs with constant coefficients and the right-hand side of the ODE cannot be an arbitrary function. (iv) The particular solution of the ODE y′′ − 6y′ + 9y  =  6e3x is given by yp  =  Cxe3x where C is an undetermined constant. (v) We must rethink what we mean by solving y′′ + y′ − y  =  { cos(x + 28) x  ≠  1 0 x  =  1 before trying to compute a solution defined on an interval containing x  =  1. (vi) A Taylor series is a power series that gives the expansion of a function around a point a. Convergence of such series is fully understood by means of the ratio test. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True,False,False,True,False,True then you would enter '1,2,2,1,2,1' into the answer box below (without the quotes).

Answer 1

are ! Answers (ii) Terue (ii) Teme (iv) False 32 y" - 64' + 9 = 60 A. E is m² 6m+ 9:0 = (n-3)2 = 0 = m-3,3 is y = (C, +62) e 3 P. I = p = 3a I 6. é 6. en (0-32 6. 1² e = 3.x² e 32 32 2 (w) Tune (vi) True. Answer 1 1 2 1 1