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Diff. eqn + erf (error function)

  • Thread starter veronik
  • Start date
5
0
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
 

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