12. All the roots of the indicial equation of the following differential equation are: (8 Puan)...

Question

Question

12. All the roots of the indicial equation of the following differential equation are: (8 Puan) By + xy + (x-1)y = 0 O and 1

math Advanced-Math

Answer 1

Answer #1

Solutiont xs” +33 + x - 2 = 0 Now, Compare the given equation witht x²y plate y +8(x) y = 0 then, PLx) = 1 -> Pool 8(x)=x-

Answer 2

Similar Homework Help Questions

12. All the roots of the indicial equation of the following differential equation are: * (8...

12. All the roots of the indicial equation of the following differential equation are: * (8 Puan) x?y" + xy' + (x - 1)y = 0 O 0, 1, -1 O and -1 0 and 1 0 1 and -1 none of these
QUESTION 9 Letr and r2 be two indicial roots of the differential equation 2x(x - 1)y"-(x...

QUESTION 9 Letr and r2 be two indicial roots of the differential equation 2x(x - 1)y"-(x +1)y'+y=0. Then ri+r2-rr- True False
In each of Problems 1 through 6: a. Show that the given differential equation has a regular singu...

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....

In each of Problems 1 through 6: a. Show that the given differential equation has a regular singu...

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....
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...

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...
(a) 5. Make up a differential equation that will have as the roots of its indicial...

(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

1 point) Consider the differential equation which has a regular singular point at x = O. The indi...

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...
6: Problem 4 Previous Problem List Next (1 point) Consider the differential equation which has a ...

6: Problem 4 Previous Problem List Next (1 point) Consider the differential equation which has a regular singular point at x = O. The indicial equation for x = 0 is rt with roots (in increasing order) ri- Find the indicated terms of the following series solutions of the differential equation: (a) y = x,16+ and rE x+ The closed form of solution (a) is y 6: Problem 4 Previous Problem List Next (1 point) Consider the differential equation which...
show that the equation xy"+y'-y=0 has a regular singular point at x=0, find the indicial equation...

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 ?

(1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has a regular singular...

(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...