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Linear and Bernoulli First Order

  1. Aug 22, 2009 #1
    1. The problem statement.

    1. http://img194.imageshack.us/img194/3815/linear.png [Broken]

    2. http://img25.imageshack.us/img25/1543/bernoulli1.jpg [Broken]

    3. http://img23.imageshack.us/img23/7991/bernoulli2.jpg [Broken]

    2.Relevant equations

    Problem 1 is Linear Differential Equation and Problems 2 and 3 are Bernoulli's D.E.

    LDE is given by: dy/dx + yP(x) = Q(x)
    BDE is given by: dy/dx + yP(x) = Q(x)y^n

    3. The attempt at a solution

    On those three equations, I'm trying to make the equations as exactly to the format on the LDE and BDE. However, I cannot get P(x) and Q(x) on no.1. The y is always y^3. In no.2, there will be Q(x)y^n and there is no y. In no.3, I solved that. However, that problem is BDE and I solved it using LDE with dx/dy. Do you think there is something wrong with the equation?

    Thank you.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 23, 2009 #2
    I think I solved the three equations. There's something wrong with those equations. The first problem can be solved by using Bernoulli but it is under the linear problem set. I got the same answer exactly as the provided answer. The second problem is Bernoulli. I modified the equation and when I solved it, I got the same answer exactly as the provided answer. The equation goes 2x^3y'=y(y^2+3x^2). The third problem is the same as the first. Instead of Bernoulli, it is solvable using Linear. Anyway, thank you.
     
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