Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For an autonomous first order ODE,  give an algorithm to compute a rational general solution if it exists. The algorithm is based on the relation beten rational solutions of the first order ODE and rational parametrizations of the plane algebraic curve defined by the first order ODE and Pade approximants.
['Ruyong Feng', 'Xiao-Shan Gao']
I am writing a research paper on a idea Rational general solutions of algebraic ordinary differential equations
[{"from": "human", "value": "I am writing a research paper on a idea Rational general solutions of algebraic ordinary differential equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For an autonomous first order ODE,  give an algorithm to compute a rational general solution if it exists. The algorithm is based on the relation beten rational solutions of the first order ODE and rational parametrizations of the plane algebraic curve defined by the first order ODE and Pade approximants."}]