The Factorizable Solution of a Class of Differential Equations
The factorization of meromorphic solutions to six typical first order algebraic differential equations has always been a concern of many authors.The factorization of the third type of first order algebraic differential equations(f')3=a0(z)(f-τ1)2(f-τ2)2(f-τ3)2 under transcendental coefficients is mainly studied,where a0(z)is a meromorphic function and τ1,τ2,τ3 is a discriminative complex number.It is proved that if f(z)=h(g(z)),whereh(z)is a meromorphic function and g(z)is a transcendental integer function,then at most,except for a point set with zero logarithmic density E,there is T(r,g)=O(T(r,a0)).
meromorphic functionfactorizable solutionupper logarithmic density
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