Points) Use the differential equation (x-x- 12 following questions: (a) Find all singular points ...
please help to solve this differential equation. 3. Use power series solutions to solve (x+1)y"+(x-2)y' +y = 0. Center the power se- ries about the ordinary point o = 0. Write the solution as y = col first four terms..]+ ciſfirst four terms...). 4. Find the minimum radius of convergence for a power series solution to the ODE (22+2x+5)/' +10y = 0 centered about the ordinary point Xo = -6
11. +-2 points ZlIDIMEQModAp11 6.2.001 My N Without actually solving the given differential equation, find the minimum radius of convergence R of power series solutions about the ordinary point x0. About the ordinary point x 1 x-0) R= (x= 1) R- Need Help?Read ItTalk to a Tutor Save Progress」 ! Submit Answer Practice Another Version
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
show work please For the given DEs, a. Indicate any singular points. b. Find the minimum radius of convergence of the power series solutions about the ordinary point x- 2 For the given DEs, a. Indicate any singular points. b. Find the minimum radius of convergence of the power series solutions about the ordinary point x- 2
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....
Consider the differential equation xy" + y + y = 0. Find a series solution for the differential equation about the regular, singular point xo = 0.
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 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...
Find all the regular singular points of the given differential equation. x?y" – x (6 + x)y' +(6+x?)y = 0 If necessary, enter your answers separated by commas. If there is no regular singular point, enter NA. X=
(Singular Points) (a) Classify the singular points of the differential equation (22 – 1)?y" + (x + 1)y' – y = 0. (b) Determine the indicial equation for the regular singular point(s) found in part (a). Also find the corresponding exponents of the singularity for those points.