2. Solve each of these ODEs using power series method expanded around Xo = 0. Find the recurrence relation and use it to find the first FOUR terms in each of the two linearly independent solution. Express your answer in general form where possible (well, it is not always possible). (a) (25 marks) (x2 + 2)y” - xy + 4y = 2x - 1-47 Note: expressa in terms of power series. (b) 2x2y" + 3xy' + (2x - 1) =...
Use the binomial series to expand the function as a power series. f (x) = 5/1+ -5/1+ 6 15(-1)*+1 (0) 2n! IM n=0 00 5 5+ 12+ + [51-1)^-1 (a)" 2n! n=2 72 5+ =1041.32... (2n – 1) () 72 5+ 5(-1)"1.3.5. .... (2n - 3) 2n! n=2 (2n – 3) 72 5 5+ - + 12" 5(-1)n-11.3.5.... 2n! n=2 State the radius of convergence, R. (If the radius of convergence is infinity, enter INFINITY.) R = X Need Heln2...
pls show work & do not use l’hopital
lim tan(5x) xo In(1 +8x)
lim tan(5x) xo In(1 +8x)
1 Problem 7 We know that we can expand as a power series for -1 < < 1. 1+2 Follow the given steps to manipulate this power series to derive the power series representation for f(x) = tan-(2) centered at a = 0. • Make the appropriate substitution to find a power series for g(x) 1/(1 + x2). • Either integrate or differentiate the previous power series to find a power series for f(x) = tan-'(x). Has the radius of...
The initial value of the flip flop outputs {X5,X4,X3.X2.X1.XO} = (1, 0, 1, 1, 0, 1) before any clock pulses. What would it be following 3 following 3 clock pulses? DX5 0x40x30x240 x10 x0- CLK CLK Shift pulses 9 [X5,X4X3X2,X1,XO} = {1, 1, 1, 1, 0, 1} 0 (X5X4X3,X2X1,XO} = (0, 0, 1, 1, 0, 1] 6 X5,X4,X3,X2X1XO) = (0, 0, 0, 1, 0, 1] o X5,X4X3,X2,X1,XO) = (1,0, 1, 0, 0, 0)
please solve with power series. part b for 2and 3 is what im really
struggling with
Question 5 (60 points) For the following first order ODE: 1) x'y' + (3x - 2y = 0, Xo = 0 DO 3X2 @O 2) (1-x)y + 2y = 0, xo = 0 3) (x^ - 6x + 10)y +(12 - 4x2y = 0, Xo = 3 a) What are the points of singularity for each specific problem? We undefined b) Does this ODE...
1. Find the first three nonzero terms in a power series expansion about Xo = 0 of the general solution of the differential equation y" + (x - 1)y = 0. Hint: Compute up to 04.
1. Find the first three nonzero terms in a power series expansion about Xo = 0 of the general solution of the differential equation y" + (x - 1)y = 0. Hint: Compute up to 01.
Can anybody show me how to solve this please? I am struggling
with power series. Thank you
(1 point) Consider the function 1 – x5 , 3" x2n, you would write en=0 Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were 1+ 3x2 + 32 x4 + 33 x6 + 34 x8. Also indicate the radius of convergence. Partial Sum: 1+5x^5+25x^10 Radius of Convergence:
Differential equations
Find the first four nonzero terms in a power series expansion about xo - 2 for the solution to the given initial value problem
Find the first four nonzero terms in a power series expansion about xo - 2 for the solution to the given initial value problem