# Solving ordinary differential equations using the differential operator D

I know how to solve linear homogeneous ordinary differential equations with constant coefficients using the differential operator D, by using this method.

Is it possible to use a similar method (using the differential operator) to solve more advanced ODEs? I'm thinking of both more advanced linear ODEs, such as Euler-Cauchy differential equations, as well as non-linear ODEs.

Are there any articles on the web on this topic, or even textbooks that use this method to solve ODEs?

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Sure; for example, the Laplace equation in two variables can be solved by factoring d/dx^2 + d/dy^2 as (d/dx + i d/dy)(d /dx - i d/dy), which gives a direct connection to the Cauchy-Riemann equations. –  Qiaochu Yuan Feb 23 '11 at 20:46