Thread: 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

Originally Posted by mobius2000

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..

Originally Posted by mobius2000

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 where are continous on an interval then there exists an analytic solution to this differencial equation.