# Math Help - ODE - Method of Frobenius

1. ## ODE - Method of Frobenius

Consider the differential equation $z^3{w}^{''}+z{w}^{'}+{\lambda}{w}=0$, where $\lambda$ is a constant.

By considering a solution of the Frobenius form, I have found that their is only one root of the indicial equation, but I cannot show that the series solution terminates, producing a solution with a finite number of terms.

Can anyone help here?

2. ## Re: ODE - Method of Frobenius

Hi !

This ODE is of the confluent hypergeometric kind.
Confluent Hypergeometric Differential Equation -- from Wolfram MathWorld
Infinite series expension are provided through the reference above.

3. ## Re: ODE - Method of Frobenius

Thanks.

I've managed to solve this now.