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The functional equations $ f^2+g^2=1 $ and $ f^2+2\alpha fg+g^2=1 $ arerespectively called Fermat-type binomial and trinomial equations. It is ofinterest to know about the existence and form of the solutions of generalquadratic functional equations. Utilizing Nevanlinna's theory for severalcomplex variables, in this paper, we study the existence and form of thesolutions to the general quadratic partial differential or partialdifferential-difference equations of the form $ af^2+2\alpha fg+b g^2+2\betaf+2\gamma g+C=0 $ in $ \mathbb{C}^2 $. Consequently, we obtain certaincorollaries of the main results of this paper concerning binomial equationswhich generalize many results in [\textit{Rocky Mountain J. Math.}\textbf{51}(6) (2021), 2217-2235] in the sense of arbitrary coefficients.

Transcendental entire solutions of several general quadratic type PDEs and PDDEs in $ \mathbb{C}^2 $