v e Course: MATH 2 X HW6.pdf X Fluid Mechanics X (11) Solved Prot X (11) conservation X Library Genesis: X (11) Mechanical x |New Tab X X C 2 eclass.srv.ualberta.ca/pluginfile.php/10652643/mod_resource/content/3/HW6.pdf DID A : HW6.pdf 1 1 228% 1. (10 points) Determine a recurrence relation for the coefficients in the power series about xo = 0 for the general solution of (1 - x2 ) y" ty' + 2y = zel. Use this to write the first five terms (i.e., all terms up to order x inclusive) of the general solution. 2. Power series solutions can be used to solve linear differential equations of any order, though this is not always the best method. (a) (7 points) Consider the first-order differential equation y' + xy = 0 with initial condition y(1) = 1. Write the solution as a power series y(x) = _ an(x - 1)" about xo = 1. Find n=0 the recurrence relation for the coefficients an and write the first four nonzero terms of y. (b) (3 points) Solve this problem by earlier (Chapter 2) methods, using the fact that this DE is either separable or linear. 3. (a) (5 points) Find all singular points in the complex plane for the linear differential equation (3+ 22 ) xy" + 2xy' + x2y = 0. (h) (k nointal If ann attaments to ankern the initial len nonblam ( 2 1 22ball I 21 1 n Temps to rise Q Search 99+ ENG 1:28 PM Thursday US 2024-03-05 PRE