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Riccati Equation

  1. Mar 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the general solutions of the following 1st-order DE: y' = by2+(1/4bx2) where b ≠ 0 is a constant.

    2. Relevant equations
    Now this is a Riccati Equation, I know that. In my math class we've only learned to solve DEs the following ways:
    a. Separation of Variables
    b. Substitution
    i. Polynomial Substitution
    ii. Homogeneous Substitution
    iii. Bernoulli DE

    3. The attempt at a solution
    The first thing I did was to assume a particular solution, which I made y1 = A/x With this I found the derivative of it: y' = -A/x2 and then y2 = A2/x2

    Using these I subbed them into the original equation giving me:
    -A/x2 = bA2/x2 + 1/4bx2

    After this I solved to make it equal to zero which is:
    0 = A + bA2 + 1/4b

    From this I used the quadratic formula to get:
    A = 0 and A = -1/b

    After this I don't know where to go, I don't know if those are even right. Could anyone give me some direction and at the same time check if what I have so far is right?

    Thanks in advance
     
  2. jcsd
  3. Mar 4, 2013 #2
    Anything?
     
  4. Mar 5, 2013 #3
    Is it that hard? Haha
     
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