4. (5 pts) Use the method of Froenius to determine the indicial roots, r, for 3xy"...
Show that the indicial roots of the singularity do no differ by an integer. Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. 9x2y" + 9(x2 + x)y' + (12x - 1)y = 0 What is the radius of convergence of those series solution
Show that the indicial roots of the singularity do no differ by an integer. Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. 9x2y" + 9(x2 + x)y' + (12x - 1)y = 0 What is the radius of convergence of those series solution
5. (20 pts) For the differential equation: sume the following information (you don't need to show this). e roots of the indicial equation are ri 4 and 2--2. In addition, after substituting y t and its derivatives into the differential equation and reindexing we get: Given this information, find all Frobenius solutions for x >0. Make sure you include the "nth" term in your solution(s). If a solution does not exist for an exponent, show why. 5. (20 pts) For...
solve 4 (4) Show that the given differential equation has a regular singular point at r = 0; determine the indicial equation, the recurrence relation, and the roots of the indicial equation; find the series solution (r > 0) corresponding to the larger root: (20 points) y = 0.
show that the equation xy"+y'-y=0 has a regular singular point at x=0, find the indicial equation and its roots how many independent solutions does the equation have ?
Use the method of Frobenius to obtain linearly independent series solutions about r = 0. 1.0"y" + 1ry' + (22 – 1)y=0. Use an initial index of k = 2 to develop the recurrence relation. The indicial roots are(in ascending order) rı = .12= Corresponding to the larger indicial root, the recurrence relation of the solution is given by C = Xq-2. The initial index is k = The solution is yı = (Q10 where Q1 = + Q222 +230...
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...
(a) 5. Make up a differential equation that will have as the roots of its indicial equation (a) 1,4 (b) 3,3 (c) 1/2,2 (d) -1/2,1/2
Use the method of Frobenius and the larger indicial root to find the first four nonzero terms in the series expansion about x = 0 for a solution to the given equation for X>0 36x2y + 12x²y + 5y = 0 What are the first four terms for the series? y(x)=0-.. (Type an expression in terms of a.)
8.6.19 Question Help Use the method of Frobenius and the larger indicial root to find the first four nonzero terms in the series expansion about x=0 for a solution to the given equation for x > 0. 9x?y" + 6x?y' +2y = 0 What are the first four terms for the series? y(x) = 1 + (Type an expression in terms of a..) + ...