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Diff. eqn + erf (error function)

  1. Mar 21, 2008 #1
    I’m stacked with this problem for many days, someone can help me pleeeeease:

    (a) [tex]f \left( x \right) =\int _{-\infty }^{{x}^{2}/2}\!{e^{x-1/2\,{t}^{2
    }}}{dt}[/tex]

    I foud the solution: [tex]f \left( x \right) =1/2\,{e^{x}}\sqrt {2\pi } \left( 1+{\it
    erf} \left( 1/4\,{x}^{2}\sqrt {2} \right) \right) [/tex]

    (b) Find the solution of the dfferential equatio:
    [tex]{\frac {d^{2}}{d{x}^{2}}}y \left( x \right) =f \left( x \right) [/tex] with y(0)=0 and dy(0)/dx = 0

    In the form : [tex]y \left( x \right) =\int _{0}^{x}\! \left( x-t \right) f \left( t
    \right) {dt}[/tex]



    Veronica
     
  2. jcsd
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