Question

Exercise 7.3.8: In the following equations classify the point x = 0 as ordinary, regular singular,...

Exercise 7.3.8: In the following equations classify the point x = 0 as ordinary, regular singular, or

singular but not regular singular.

a) x2(1+x2)y′′ +xy=0

b) x2y′′ +y′ +y=0

c) xy′′ +x3y′ +y=0

d) xy′′ +xy′ −exy=0

e) x2y′′ +x2y′ +x2y=0

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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 =
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
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
[Cauchy-Euler equations] For the following equations with the unknown function y = y(x), find the general...
[Cauchy-Euler equations] For the following equations with the unknown function y = y(x), find the general solution by changing the independent variable x to et and re-writing the equation with the new unknown function v(t) = y(et). x2y′′ +xy′ +y=0 x2y′′ +xy′ +4y=0 x2y′′ +xy′ −4y=0 x2y′′ −4xy′ −6y=0 x2y′′ +5xy′ +4y=0.
Consider differential equation: x3 (x2-1)2 (x2+1) y'' + (x-1) x y' + y = 0 .....
Consider differential equation: x3 (x2-1)2 (x2+1) y'' + (x-1) x y' + y = 0 .. Determine whether x=0 is a regular singular point. Determine whether x=1 is a regular singular point. Are there any regular singular points that are complex numbers? Justify conclusions.
Find at least one solution about the singular point x = 0 using the power series...
Find at least one solution about the singular point x = 0 using the power series method. Determine the second solution using the method of reduction of order. xy′′ + (1−x)y′ − y = 0
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
A Non-Constant Coefficient ODE: Solve the non-constant coefficient ordinary differential equation given below: ?2?2???2−34?=0, subject to...
A Non-Constant Coefficient ODE: Solve the non-constant coefficient ordinary differential equation given below: ?2?2???2−34?=0, subject to the boundary conditions (not initial conditions) ?(0)=0,?(1)=1. After solving, answer the following questions: i) Is x = 0 in the ODE a) an anomalous singular point, b) an irregular singular point, c) a regulous singularious point. d) a regular singular point? ii) If the coefficient “x2” were replaced with “x3/2” which solution series below would you use? a) ?=Σ????∞?=0, b) ?=Σ??+???+?∞?=0, s a constant,...
X, Y, Z are 3 independent random variables. We know that Y, Z is the 0-1...
X, Y, Z are 3 independent random variables. We know that Y, Z is the 0-1 random variables indicating whether tossing a regular coin gets a head (1 means getting a head and 0 means not). We also know the following equations, E(X2Y +XYZ)=7 E(XY 2 + XZ2) = 3 Please calculate the expectation and variance of variable X.
Solve the following non homogenous Cauchy-Euler equations for x > 0. a. x2y′′+3xy′−3y=3x2. b. x2y′′ −2xy′...
Solve the following non homogenous Cauchy-Euler equations for x > 0. a. x2y′′+3xy′−3y=3x2. b. x2y′′ −2xy′ +3y = 5x2, y(1) = 3,y′(1) = 0.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT