The paper describes the general form of an ordinary differential equation of the order $n+1$ $(n\ge 1)$ which allows a nontrivial global transformation consisting of the change of the independent variable. A result given by J. Aczél is generalized. A functional equation of the form $$f\left(s,v,w_{11}{v}_1,...,\sum _{j=1}^n{w}_{nj}{v}_j\right)=\sum _{j=1}^n{w}_{n+1j}{v}_j+w_{n+1n+1}f(x,v,v_1,...,v_n),$$ where $w_{ij}=a_{ij}(x_1,...,x_{i-j+1})$ are given functions, $w_{n+11}=g(x,x_1,...,x_n)$, is solved on $ℝ.$

For linear differential and functional-differential equations of the $n$-th order criteria of equivalence with respect to the pointwise transformation are derived.

The paper describes the general form of functional-differential equations of the first order with $m(m\ge 1)$ delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation $$f(t,uv,u_1{v}_1,...,u_m{v}_m)=f(x,v,v_1,...,v_m)g(t,x,u,u_1,...,u_m)u+h(t,x,u,u_1,...,u_m)v$$ for $u\ne 0$ is solved on $ℝ$ and a method of proof by J. Aczél is applied.

The paper describes the general form of an ordinary differential equation of an order $n+1$ $(n\ge 1)$ which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form $$f\left(s,w_{00}{v}_0,...,\sum _{j=0}^n{w}_{nj}{v}_j\right)=\sum _{j=0}^n{w}_{n+1j}{v}_j+w_{n+1n+1}f(x,v,v_1,...,v_n),$$ where $w_{n+10}=h(s,x,x_1,u,u_1,...,u_n)$, $w_{n+11}=g(s,x,x_1,...,x_n,u,u_1,...,u_n)$ and $w_{ij}=a_{ij}(x_1,...,x_{i-j+1},u,u_1,...,u_{i-j})$ for the given functions $a_{ij}$ is solved on $ℝ$, $u\ne 0.$