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Differential equations help

  1. Oct 9, 2013 #1
    1. The problem statement, all variables and given/known data

    Solve each of these differential equations by two different methods.

    [tex] \frac{dy}{dx} = 4(y+1)x^3[/tex]


    2. Relevant equations

    Integrating factor

    [tex] \rho = \exp (\int(p(x) dx)[/tex]

    Linear Equation

    [tex] \frac{dy}{dx} + p(x) y(x) = Q(x) [/tex]


    3. The attempt at a solution

    So I first solved it using separation. I get [tex] y=A \exp(x^4) -1 [/tex]

    I then try to solve it using Integrating factors.

    [tex] \frac{dy}{dx} + - 4x^3 y=4x^3 [/tex]
    [tex] \rho = \exp (\int -4x^3 dx) = exp(-x^4) [/tex]

    Multiplying through by the integrating factor I get.

    [tex] \exp(-x^4) y= \int 4x^3 exp(-x^4) dx [/tex]

    but when I solve it, I get

    [tex] y = -1 [/tex]


    What can I be doing wrong? I checked my steps multiple times.
     
  2. jcsd
  3. Oct 9, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are forgetting the constant of integration on ##\int 4x^3 exp(-x^4) dx##.
     
  4. Oct 9, 2013 #3
    Oh yeah!! I knew it was something so simple. Thank you very much! :)
     
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