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Y(x) = x/(1+cx) ; dy/dx = y^2/x^2

  1. Jun 8, 2010 #1
    1. The problem statement, all variables and given/known data

    Show that each function in the family satisfies the differential equation.
    y(x) = x/(1+cx) ; dy/dx = y^2/x^2


    3. The attempt at a solution

    I'm not sure where to start. I can't see how the integral of dy/dx = y(x)
     
  2. jcsd
  3. Jun 8, 2010 #2
    Start by taking dy/dx of your y(x) equation, then compare that to y^2/x^2. What do you get?
     
  4. Jun 8, 2010 #3
    thanks for the reply.

    y(x) = x/(1+cx)

    dy/dx = ((1+cx) - xc)/(1+cx)^2 = 1/(1+cx)^2

    So how does that equal y^2/x^2
     
  5. Jun 8, 2010 #4

    D H

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    What is y^2/x^2?
     
  6. Jun 8, 2010 #5
    I'm not sure what you mean. This is all the information i was given for the problem.
     
  7. Jun 8, 2010 #6
    You have solved dy/dx given that you had started with y(x). That is, you solved the left side of dy/dx = y^2/x^2. Now you have to solve the right side. y^2 = (y(x))^2, try plugging in y(x) to the RHS of that equation and see if the two match up.
     
  8. Jun 8, 2010 #7
    Click, so you mean,

    y^2/x^2 = 1/(1 cx)^2

    y^2 = x^2/(1+cx)^2

    sqrt(y^2) = sqrt(x^2/(1+cx)^2) = sqrt((x/(1+cx))^2))

    y = x/(1+cx)
     
  9. Jun 8, 2010 #8
    Yes :). But in this case it suffices to just show that y^2/x^2 is the same as dy/dx, which you did in the first step.
     
  10. Jun 8, 2010 #9
    Alright. Thanks for the help, it is greatly appreciated.
     
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