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Math Help - series soultions to differential equations

  1. #1
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    series soultions to differential equations

    what are the requirements of a differential equation for its solution to be a power series? the function has to be analytic; what exactly does this mean? does the right hand side always have to equal zero as well?

    thanks
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    Quote Originally Posted by mobius2000 View Post
    what are the requirements of a differential equation for its solution to be a power series? the function has to be analytic; what exactly does this mean? does the right hand side always have to equal zero as well?

    thanks
    Analytic just means it can be locally defined by a power series..
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    Quote Originally Posted by mobius2000 View Post
    what are the requirements of a differential equation for its solution to be a power series? the function has to be analytic; what exactly does this mean? does the right hand side always have to equal zero as well?
    The simple version says that if you have y''+p(x)y'+q(x)y=0 where p(x),q(x) are continous on an interval I then there exists an analytic solution y to this differencial equation.
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