Let \(K={\mathbb R}\) or \({\mathbb C}\), \(U\) an open subset of \(K^n\), \(\mu: U\rightarrow K\) and \(f,g: U\rightarrow K^n\) analytic functions, and consider the differential equation \(\dot x =f(x)+\mu(x)g(x)\). The main result of the paper describes how the general solution of this equation is expressible in terms of the solutions of \(\dot x= f(x)\) and \(\dot x=g(x)\), whenever the vector fields \({1\over \mu}f\) and \(g\) commute. This result is applied to construct a class of additive group actions on affine spaces that are proved to be stably tame and to give explicit solutions of a class of quadratic equations \(\dot x= x^2+\alpha\omega(x)x\), where \(x^2\) is a homogeneous quadratic polynomial map (and hence the square of \(x\) in a commutative nonassociative algebra defined on \(K^n\)), \(\alpha\) is a nonzero scalar and \(\omega: K^n\rightarrow K\) a homomorphism of algebras. In particular, this covers some differential equations used to describe population models in genetics [see the monograph by \textit{A. Wörz-Busekros}, Algebras in genetics. Springer Lecture Notes in Biomathematics 36 (1980; Zbl 0431.92017)].