4. Show that ΣΕǐrk is a solution to y" +/-2-0. (a) Find the general series solution to the DE 2rz...
Consider the ODE:3xy"+y' - 2xy = 0. Find the general solution in power series form about the regular singular point x = 0, following parts (a) – (c), below. (a) Obtain the recurrence relation. (b) Find the exponents of the singularity. (e) Obtain only one of the two linearly independent solutions, call it y(x), that corresponds to the smaller exponent of the singularity; but, only explicitly include the first four non-zero terms of the power series solution. Write down the...
I. Let 2r2y"-ry' + (r' + 1) y = 0. ) Verify that a 0 is a regular singular point. (2 points) ) Find two linearly independent power series solutions about a0. Provide at least3 aon-zero terms of each solution. (8 points) 0 0 is reowlar 터 -2 kti I'm Stuck-HEKG-HER- ME FINISH I. Let 2r2y"-ry' + (r' + 1) y = 0. ) Verify that a 0 is a regular singular point. (2 points) ) Find two linearly independent...
please show the recurrence formula 1) Show that zo-0 is a regular singular point for the diferenta equation Zo = 0 is a regular singular point for the differential equation 15ェy" + (7 + 15r)y, +-y = 0, x>0. Use the method of Frobenius to obtain two linearly independent series solutions about zo Find the radii of convergence for these series. Form the general solution on (0, 0o). 0. 1) Show that zo-0 is a regular singular point for the...
Consider the differential equation xy" + y + y = 0. Find a series solution for the differential equation about the regular, singular point xo = 0.
2. Using the method of Frobenius, find the general solution about the point i = 0 of the ordinary differential equation 1 (1 - 4) y" - ry' +y = 0. Simplify your answer as much as possible and state the domain of validity. 110 3. Consider the general series solution about the point I = 0 of the ordinary differential equation e'y' + 2y = 0. Find the coefficients of all the terms of this series solution up to...
Question 2 In this question you need to construct a homogeneous linear second order differential equations satisfying particular things . The DE has a regular singular point at 1 and an irregular singular point at 3 X2 Is a solution The DE has a regular singular point at x 0 and y Question 3 Identify the regular singular points and compute their indicial roots of the following DEs Question 3 Find a series solution of ry" - (3x - 2)y...
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) =...
Given the DE: y"-(x+1)y'-y=0 use it to answer the following: a) Find the singular point(s), if any, and if lower bound for the radius of convergence for a power series solution about the ordinary points x=0 b)The recurrence relation Hint: It will be a 3-term recurrence relation c)Give the first four non-zero terms of each of the two linearly independent power series solutions near the ordinary point x=0
2. Find power series solutions y z" Σ anr" of the following equation centered at 0 where-0 is a regular singular point. (a) Find the indicial equation for r, and solve for the two roots. Note that the indicial equation can be obtained from the coefficients of the term Pick the larger root and find the first seven terms of your power series solutions, i.e., (b)
(Example 6.3.2) Find the general solution of the differential equation 5. in series centered at the regular singular point 0