Results 1 to 3 of 3

Math Help - Help solving xy" - y' = 3x^2

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    5

    Help solving xy" - y' = 3x^2

    I am a first time differential equations student so I will try my best.

    By observation, I have a second order de with non-constant coefficients. Normally with a question like this, I would first attempt the Cauchy-Euler method (substitute y=x^m), and then use variation of parameters to find the particular solution.

    However, in this case the power of x does NOT match the degree of derivation of y (x is power one, y is 2nd derivative) and substituting y=x^m comes out with something that doesn't seem quite right to me.

    I thought of dividing through by x and finding and integrating factor, but then realized it is not in the correct form to do so.

    If someone could help me to find the general solution I'm fairly sure I could tackle the particular one.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by LucasV View Post
    I am a first time differential equations student so I will try my best.

    By observation, I have a second order de with non-constant coefficients. Normally with a question like this, I would first attempt the Cauchy-Euler method (substitute y=x^m), and then use variation of parameters to find the particular solution.

    However, in this case the power of x does NOT match the degree of derivation of y (x is power one, y is 2nd derivative) and substituting y=x^m comes out with something that doesn't seem quite right to me.

    I thought of dividing through by x and finding and integrating factor, but then realized it is not in the correct form to do so.

    If someone could help me to find the general solution I'm fairly sure I could tackle the particular one.
    Divide through by x. Substitute y' = u. Solve for u using integrating factor method. Then get y from u.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    5
    Thanks! I was at school all day and didn't get a chance to try this until now, but it worked beautifully. I took the first and second derivatives of my result and plugged them into the ode. Low and behold, the result was equal to the right hand side of 3x^2! Thanks again for your help. Solved.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving for unknown "x" involving trig function
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: August 27th 2010, 04:59 AM
  2. Replies: 2
    Last Post: August 6th 2010, 08:26 PM
  3. Replies: 4
    Last Post: March 29th 2010, 04:05 PM
  4. Replies: 0
    Last Post: October 6th 2009, 11:29 AM
  5. Replies: 4
    Last Post: November 3rd 2007, 04:33 PM

/mathhelpforum @mathhelpforum