Determine whether x=0 is a regular singular point of the differential equation 2x²y"+xy'+(x²-1)y=0.hence find the general solution near x=0
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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...
(1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has a regular singular point atx 0. The indicial equation for x 0 is 2+ 0 r+ with roots (in increasing order) r and r2 Find the indicated terms of the following series solutions of the differential equation: x4. (a) y =x (9+ x+ (b) y x(7+ The closed form of solution (a) is y (1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has...
A. Find the singular points of given differential equation. Determine whether the singular points are regular or irregular singular point. (x-1)xºy" +2xy' + [(cos3x - 1)/x]y = 0 (1 - x?)y" + [3x/(5 + 3x)]y' - (1 + xº)y = 0
4. Given that x =0 is a regular singular point of the given differential equation, show that the indicial roots of the singularity do not differ by an integer. Use the method of Frobenius to obtain to linearly independent series solutions about x = 0. Form the general solution on (0, 0) kxy” – (2x + 3)y' + y = 0
1. Write the forms of the series expansion about the regular singular point x=0 for two linearly independent solutions to the following differential equation (do not compute the coefficients in the expansions): zºy'(x) - xy'(x) + (1 - x)y(x) = 0. (1) 2. Does the following system of equations have an unique solution? Explain your reason for the answer (do not find the solution). 2x 1 + 4x2 + x3 = 8 2x + 4.62 = 6 -401 - 8x2...
1 point) Consider the differential equation which has a regular singular point at x = O. The indicial equation for x 0 is r1/2 r+ 0 =0 and r O with roots (in increasing order) r1/2 Find the indicated terms of the following series solutions of the differential equation: (a) y = x, (94 (b)y-x(5+ The closed form of solution (a) is y = xtO r3+ 1 point) Consider the differential equation which has a regular singular point at x...
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....
Given that x =0 is a regular singular point of the given differential equation, show that the indicial roots of the singularity do not differ by an integer. Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on (0, ∞) 2xy''-y'+y=0
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...
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....