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Homework Help: Seperation of variable differential

  1. Jul 24, 2011 #1
    1. The problem statement, all variables and given/known data

    2y dy/dx = xy^2 + x

    y(0)= 2

    3. The attempt at a solution

    the first step i did was take out the x on the right for x(y^2+1)

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

    then shift things around

    2y/(y^2+1) dy = x dx
    then integrate
    u substitution gives

    ln y^2+1 = 1/2 x^2 + C

    turn e^c into A

    y^2+1 = A e^ 1/2 x^2

    now my algebra and other stuff gets rusty and dnt know if im right

    y= sqrt ( A e^(1/2x^2) - 1

    with y(0) = 2 i multiply the A and (e^0) 1 first right? then subtract 1 . so A=5?
    .x=0 y=2.

    so would the final answer be y=sqrt(5e^(1/2x^2)+1)

    i got a = 4 the first time but thought my math was wrong.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jul 24, 2011 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes, A = 5.

    So, y = sqrt{5e^(x2/2) - 1}

    You changed the sign on the 1 when you wrote your final result.
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