Take an equation
$$w'+w-w^2-1=0$$
Its solution is
$$w(x)=\frac{\sqrt{3}}{2} \tan \left( \frac{\sqrt{3}}2 C+\frac{\sqrt{3}}2 x\right)+\frac12$$
I wonder why a similar difference equation
$$\Delta w+w-w^2-1=0$$
cannot be solved?
Take an equation
$$w'+w-w^2-1=0$$
Its solution is
$$w(x)=\frac{\sqrt{3}}{2} \tan \left( \frac{\sqrt{3}}2 C+\frac{\sqrt{3}}2 x\right)+\frac12$$
I wonder why a similar difference equation
$$\Delta w+w-w^2-1=0$$
cannot be solved?