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Some ODE help needed

  1. Feb 3, 2009 #1
    So this question pertains to some process engineering homework i have, which is basically the following:

    I have an ODE that has the form: [tex]\frac{dh^{p}}{dt}[/tex]+h[tex]^{p}[/tex]+[tex]\int h^{p}[/tex]=F[tex]^{p}[/tex]{t}
    where F[tex]^{p}[/tex]{t} is the unit ramp function (i.e. F[tex]^{p}[/tex]{t}=0 when t<0, and is equal to t when F[tex]^{p}[/tex][tex]\geq[/tex]0

    So my question is how do i solve this ODE without using Laplace transforms?? Can there even be an integral in such an ODE??

    Thanks in advance, i appreciate your help
     
  2. jcsd
  3. Feb 5, 2009 #2
    We can remove the integral sign by differentiating the equation with respect to t

    h" + h' + h = F'(t)

    This is a nonhomegeneous linear DE with constant coefficients which can be solved quite easily without using the Laplace transform.
     
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