# Thread: series soultions to differential equations

1. ## 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

2. 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..

3. 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 $\displaystyle y''+p(x)y'+q(x)y=0$ where $\displaystyle p(x),q(x)$ are continous on an interval $\displaystyle I$ then there exists an analytic solution $\displaystyle y$ to this differencial equation.