On the functional equation $f^n(z)+g^n(z)=e^{\alpha z+\beta }$

We describe meromorphic solutions to the equations $f^n(z)+{\left(f^{\mathrm{\prime }}\right)}^n(z)=e^{\alpha z+\beta }$ and $f^n(z)+f^n(z+c)=e^{\alpha z+\beta}$($c\neq0$)overthecomplexplane$$\mathbf{C}$$forintegers$n\geq1$.