Question

Consider the differential equation x2y''+xy'-y=0, x>0. a. Verify that y(x)=x is a solution. b. Find a...

Consider the differential equation x2y''+xy'-y=0, x>0.

a. Verify that y(x)=x is a solution.

b. Find a second linearly independent solution using the method of reduction of order. [Please use y2(x) = v(x)y1(x)]

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
Verify that the given function is a solution and use Reduction of Order to find a...
Verify that the given function is a solution and use Reduction of Order to find a second linearly independent solution. a. x2y′′ −2xy′ −4y = 0, y1(x) = x4. b. xy′′ − y′ + 4x3y = 0, y1(x) = sin(x2).
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...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x)       dx (5) as instructed, to find a second solution y2(x). x2y'' -11xy' + 36y = 0; y1 = x6 y2 =
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order,...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order, to find a second solution dx **Please do not solve this via the formula--please use the REDUCTION METHOD ONLY. y2(x)= ?? Given: y'' + 2y' + y = 0;    y1 = xe−x
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0,...
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, ∞). Find the general solution of the given nonhomogeneous equation. x2y'' + xy' + y = sec(ln(x)) y1 = cos(ln(x)), y2 = sin(ln(x))
Consider the second-order homogeneous linear equation y''−6y'+9y=0. (a) Use the substitution y=e^(rt) to attempt to find...
Consider the second-order homogeneous linear equation y''−6y'+9y=0. (a) Use the substitution y=e^(rt) to attempt to find two linearly independent solutions to the given equation. (b) Explain why your work in (a) only results in one linearly independent solution, y1(t). (c) Verify by direct substitution that y2=te^(3t) is a solution to y''−6y'+9y=0. Explain why this function is linearly independent from y1 found in (a). (d) State the general solution to the given equation
Solve the 2nd Order Differential Equation using METHOD OF REDUCTION Please don't skip steps! (x-1)y"-xy'+y=0 x>1...
Solve the 2nd Order Differential Equation using METHOD OF REDUCTION Please don't skip steps! (x-1)y"-xy'+y=0 x>1 y1(x)=x My professor is getting y2(x)=e^x and I don't understand how!
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx     (5) as instructed, to find a second solution y2(x). y'' + 36y = 0;    y1 = cos(6x) y2 = 2) The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1...
The indicated function y1(x) is a solution of the associated homogeneous differential equation. Use the method...
The indicated function y1(x) is a solution of the associated homogeneous differential equation. Use the method of reduction of order to find a second solution y2(x) and a particular solution of the given nonhomoegeneous equation. y'' − y'  = e^x y1 = e^x
Solve the 2nd Order Differential Equation using METHOD OF REDUCTION Please don't skip steps! (x-1)y"-xy'+y=0 x>1...
Solve the 2nd Order Differential Equation using METHOD OF REDUCTION Please don't skip steps! (x-1)y"-xy'+y=0 x>1 y1(x)=x
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT