6. (a) (1 point) Take the derivative of the function n=0 observe that the first term...
(a) Show that the function defined by the power series 20+1 y=(-1)" 2n +1 n=0 satisfies the differential equation: (1+2?)y = 1. (b) Find the radius of convergence and the interval of convergence of the power series "-3 (x - 3)" 72 nao
Find two power series solutions of the given differential
equation about the ordinary point x = 0. y′′ − 4xy′ + y = 0
Find two power series solutions of the given differential equation about the ordinary point x = 0. y!' - 4xy' + y = 0 Step 1 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" - 4xy' + y = 0 By Theorem 6.2.1, we know two...
Consider the equation 3x²y" + x(2 – xy + xy = 0 with regular singular point Xo = 0. (a) Find the indicial roots ri, r2, with ri r2. Show your calculations. (b) Which of the following is true for the equation above: Indicate the letter of your choice and explain your choice. % There are two linearly independent convergent series solutions of the form yı (x) = x Š cux" and y(x) = x Š b,x". H0 N=0 (1)...
Do JUST # 3 Please
In each of Problems 1 through 6: a. Show that the given differential equation has a regular singular point at x0. b. Determine the indicial equation, the recurrence relation, and the roots of the indicial equation. c. Find the series solution (x >0) corresponding to the larger root. d. If the roots are unequal and do not differ by an integer, find the series solution corresponding to the smaller root also. 2. xy" +xy+ 3....
Do JUST # 2 please
In each of Problems 1 through 6: a. Show that the given differential equation has a regular singular point at x0. b. Determine the indicial equation, the recurrence relation, and the roots of the indicial equation. c. Find the series solution (x >0) corresponding to the larger root. d. If the roots are unequal and do not differ by an integer, find the series solution corresponding to the smaller root also. 2. xy" +xy+ 3....
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
(1 point) Use power series to solve the initia-value problem 2n+1 2n Answer: y- n-0
(1 point) Use power series to solve the initia-value problem 2n+1 2n Answer: y- n-0
Question 3 (1 point) The function f is defined by the power series 1)2 3! 5! 72n+1)! 1)% n-0 (2n+1) ! for all real numbers x. Use the first and second derivative test by finding f(x) and f"(x). Determine whether f has a local maximum, a local minimum, or neither at x=0. Give a reason for your answer. Use the
Question 3 (1 point) The function f is defined by the power series 1)2 3! 5! 72n+1)! 1)% n-0 (2n+1)...
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...
20. 0/2 points | Previous Answers ZillDiffEQ9 6.3.018 The point x 0 is a regular singular point of the given differential equation. 4x2y"-xy + (x2 + 1)y = 0 Show that the indicial roots r of the singularity do not differ by an integer. (List the indicial roots below as a comma-separated list.) Use the method of Frobenius to obtain two linearly independent series solutions about x-0. Form the general solution on (0, ) 2015 340**. y = C-X1/4 1672...