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Y''=-(t^2)y differential equation

  1. Apr 22, 2014 #1
    Hello I was recently working on a problem where I had to solve the differential equation in the title ( where y is a function of t), I found an exact series solution through peturbation theory in which a pattern emerged between successive orders.
    However, the series solution is not very useful for computation and I would like to ask if anyone knew a special function which solved this equation?
     
  2. jcsd
  3. Apr 22, 2014 #2

    hilbert2

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  4. Apr 22, 2014 #3
    You can also use the change of variable t^2=x, the resulting differential equations is a modified Bessel equation for x whose solutions are modified Bessel Functions.
     
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