Solve the differential equation below using series methods. y' + 3xy' + 8y = 0, y(0)...
Solve the differential equation below using series methods. y” – 2xy' – y = 0, y(0) = 3, y'(0) = - – 8 Find the first few terms of the solution y(x) = 2 azxk k=0 ao Preview ai Preview a2 Preview a3 Preview 24 Preview 25 Preview Points possible: 1 License
Solve the differential equation below using series methods. (4x2 + 3)y” – 6xy = 0, y(0) = 3, y'(0) 4 Find the first few terms of the solution 00 y(x) = anak k=0 ao Preview a1 Preview a2 Preview a3 = Preview 04 II Preview 05 Preview
Solve the differential equation below using series methods. ( - 6x2 – 9))'' – 2xy = 0, y(0) = –6, y’ (0) = 2 Find the first few terms of the solution y(a) = È ancak k=0 Preview Preview Preview Preview Preview Preview
Solve the differential equation below using series methods: y’’ - e* y = 0, y(0) = 4, y'(0) = 3 The first few terms of the series solution are y = co + Cix + c2x2 + C30° + C4x4 + 25x® where: Preview Preview Preview IL L LL LL Preview Preview Preview
solve the differential equation using the power series For the following differential equations, find 42, 43, 44, 45, 46, and an in terms of ao and ai and write the answer y(x) = 60 sum of terms :) + sum of terms + ai 3. (2+2?)y" – xy + 4y = 0) expanding about 10 = 0.
3. Consider the following differential equation 0o and a series solution to the differential equation of the form a" n-0 (a) Find the recurrence relations for the coefficients of the power series. 3 marks] (b) Determine the radius of convergence of the power series. l mar (c) Write the first eight terms of the series solution with the coefficients written in terms of ao and ai 2 marks] 3. Consider the following differential equation 0o and a series solution to...
Consider the following initial value problem, (1 - 2)" + 3xy' - 8y = 0, 3(0) = 3, 7(0) = 0. Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals. (a) This differential equation has singular points at Note: You must use a semicolon here to separate your answers (b) Since there is no singular point at x = 0, you can find a normal power series solution for y() about...
For the given differential equation: ?>" + xy' - 3xy = 0 We seek a series solution of the form y = anam+r. Using the larger root, the recursion formula is given by 30-1 I. an+1 = n2 30n-1 II. a n? 3an-1 III. an = IV. (n+3),-1 (n + 1)n2
In this exercise we consider finding the first five coefficients in the series solution of the first order linear initial value problem (+3)y' 2y 0 subject to the initial condition y(0) 1. Since the equation has an ordinary point at z 0 it has a power series solution in the form We learned how to easily solve problems like this separation of variables but here we want to consider the power series method (1) Insert the formal power series into...
Question 4: [25 pts] Consider the differential equation y" - 4xy = 0. a) Write the general form of the power series solution around Xo = 0 and find it's first and second order derivatives. b) Approximate the given differential equation using Power Series method by finding the first five terms of the Power Series solution around Xo = 0. c) How would your solution change if we change the differential equation as y" – 8y = 0? Explain.