Si dà una semplice dimostrazione d'esistenza ed unicità di soluzioni
per un'equazione differenziale
\[
\overset{m}{\underset{\mu=0}{\sum}}\quad\overset{n}{\underset{\upsilon=0}{\sum}}\mathit{a_{\mu\upsilon}\textrm{(z}}_{1},z_{2})\mathit{D_{\textrm{1}}^{\mu}}\mathit{D_{\textrm{2}}^{\upsilon}}\mathit{w+b}(z_{1},z_{2})=0
\]
in due variabili complesse con opportuni coefficienti analitici. We give a simple proof of existence and uniqueness of solutions for
a differential equation.
\[
\overset{m}{\underset{\mu=0}{\sum}}\quad\overset{n}{\underset{\upsilon=0}{\sum}}\mathit{a_{\mu\upsilon}\textrm{(z}}_{1},z_{2})\mathit{D_{\textrm{1}}^{\mu}}\mathit{D_{\textrm{2}}^{\upsilon}}\mathit{w+b}(z_{1},z_{2})=0
\]
in two complex variables with suitable analytic coefficients.
