Question

7. Given that x =0 is a regular singular point of the given differential equation, show...

7. 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

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given that x =0 is a regular singular point of the given differential equation, show that...
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, ∞) 3xy”+(2 – x)y’ – y = 0
The point x = 0 is a regular singular point of the differential equation. x^2y'' +...
The point x = 0 is a regular singular point of the differential equation. x^2y'' + (9 /5 x + x^2) y' − 1/ 5 y = 0. Use the general form of the indicial equation (14) in Section 6.3 r(r − 1) + a0 r + b0 = 0 (14) to find the indicial roots of the singularity. (List the indicial roots below as a comma-separated list.) r =
Series Solutions Near a regular singular point: Find two linearly independent solutions to the given differential...
Series Solutions Near a regular singular point: Find two linearly independent solutions to the given differential equation. 3x2y"-2xy'-(2+x2)y=0
Consider the differential equation 4x2y′′ − 8x2y′ + (4x2 + 1)y = 0 (a) Verify that...
Consider the differential equation 4x2y′′ − 8x2y′ + (4x2 + 1)y = 0 (a) Verify that x0 = 0 is a regular singular point of the differential equation and then find one solution as a Frobenius series centered at x0 = 0. The indicial equation has a single root with multiplicity two. Therefore the differential equation has only one Frobenius series solution. Write your solution in terms of familiar elementary functions. (b) Use Reduction of Order to find a second...
Consider the differential equation x^2 y' '+ x^2 y' + (x-2)y = 0 a) Show that...
Consider the differential equation x^2 y' '+ x^2 y' + (x-2)y = 0 a) Show that x = 0 is a regular singular point for the equation. b) For a series solution of the form y = ∑∞ n=0 an x^(n+r)   a0 ̸= 0 of the differential equation about x = 0, find a recurrence relation that defines the coefficients an’s corresponding to the larger root of the indicial equation. Do not solve the recurrence relation.
Series Solution Method. Solve the given differential equation by means of a power series about the...
Series Solution Method. Solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution. (1 − x)y′′ + y = 0, x0 = 0
Differential Equation: Determine two linearly independent power series solutions centered at x=0. y” - x^2 y’...
Differential Equation: Determine two linearly independent power series solutions centered at x=0. y” - x^2 y’ - 2xy = 0
Solve the given differential equation by means of a power series about the given point x0....
Solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution. y′′ + xy = 0, x0 = 0
Consider the following differential equation 32x 2y '' + 3 (1 − e 2x )y =...
Consider the following differential equation 32x 2y '' + 3 (1 − e 2x )y = 0 (b) Determine the indicial equation and find its roots. (c) Without solving the problem, formally write the two linearly independent solutions near x = 0. (d) What can you say about the radius of convergence of the power series in (c)? (e) Find the first three non-zero terms of the two linearly independent solutions.
Use an appropriate infinite series method about x = 0 to find two solutions of the...
Use an appropriate infinite series method about x = 0 to find two solutions of the given differential equation. (Enter the first four nonzero terms for each linearly independent solution, if there are fewer than four nonzero terms then enter all terms. Some beginning terms have been provided for you.) y'' − 2xy' − y = 0
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT