2nd Order linear ODEs

I'm having trouble solving this problem:

For the equation x^(2)y′′ - xy′ = 0 , find two solutions, show that they are linearly independent and find the general solution. Hint: Try y = x^(r).

I divided the equation by x^(2) first to simplify it, and then I found the first and second derivatives of y and tried plugging them back in. But I don't know where to go from there. Please help! Thank you!

  1. 👍 0
  2. 👎 0
  3. 👁 122
  1. Hmmm. I'd let v = y'
    Then we have

    x^2 v' = xv
    v' = v/x
    dv/v = dx/x
    log v = log x + c
    v = e^c x
    or,
    v = c1 * x
    That means y' = c1 * x
    y = c1 x^2 + c2

    check:
    y' = 2c1 x
    y" = 2c1
    x^2 y" - xy' = x^2(2c1) - x(2c1 x) = 0

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    I am having trouble solving this problem: "Find where the tangent line is horizontal for r=1+cos(theta)" I would really appreciate the feedback, I'd like to know how to go about solving problems like these. Thank you!

    asked by Anonymous on March 1, 2013
  2. Math

    having trouble solving equation 8+3x6-4-1=13 can anyone help we have tried everything and it's not working out for me is that 3x or 3*6 3*6 Are you sure you put the right equation? yes. 8+3*6-4-1=13 what do the instructions say?

    asked by Cory on November 2, 2006
  3. Algebra

    I am still having trouble solving this problem. Use the quadratic formula to solve this equation: 4k(k+13)=13

    asked by Jay on April 26, 2012
  4. math

    What strategy did you use in solving this problem? 22. Suppose that you wanted to find the whole numbers represented by each of the letters in the following addition problem: Which problem-solving strategy might be most helpful to

    asked by kim on January 20, 2010
  5. Algebra 2

    Solving Quadratic Systems x^2+y^2=2 x^2-6y=10 I'm having trouble solving this problem.

    asked by Michelle on December 1, 2014
  6. 7th grade math

    c. Find x using the ratios of the sides 6cm and 8cm. Show your work. Im having trouble solving this problem, mostly because im not sure what function to use. If i could get some help on this it would be appreciated.

    asked by Space Dandy on December 15, 2015
  7. math

    Hi I need help with this math problem: The plane that contains the points (8,3,1), (2,6,3), and (4,6,2) has an equation of the form ax + by + cz = d. Find coefficients for this equation, trying two different approaches to the

    asked by jen on July 29, 2010
  8. Algebra

    Hi, I just started learning about direct, joint, and inverse variation. I was doing a practice question and got -18 when the answer is -8. I'm having trouble solving the problem because my book only shows me how to find y not x.

    asked by Algebra on April 9, 2019
  9. Math

    The problem states that "5 to 8 is as 15 to w." I'm having some trouble solving this because I am unsure of what the problem is asking me to do. Some help would be appreciated. Thank you! :)

    asked by Melisande on January 13, 2014
  10. beginning chemistry

    The problem says indicate the the number of sig. figs. that should be present in the answers to the following problem without solving the problem. 0.70 x 7.00 x 6.880= What is a sig.fig. and how can you find them without solving

    asked by Kimmi on September 19, 2007

More Similar Questions