Consider the equation

$$f'(x)+ g(x)f(x)=0$$

This equation is an ODE and has a solution $$ f(x)=C e^{ \int_1^x g(x) \ dx}.$$

Similarly, we can look at complex variables and consider the equation and Wirtinger derivatives

$$ (\partial_{\bar z} f)(z) +g(z) f(z)=0.$$

Can one still write down an explicit solution?