I try to have a general expression of a sequence of functions defined as follow :
$$u_0=f ~\text{and}~ \forall n >0, u_{n+1} =-f\times u_n + \frac{du_n}{dt} $$
where $f\in \mathcal{C}^\infty(\mathbb{R},\mathbb{R}) $. Does anyone know how to compute the expression of $u_n$, a method or a problem related ?
I already try to figure out a expression based on the first terms but I struggle to generalize it...
Thank you very much in advance !
If $g'=-fg$ and $v_n=u_ng$ then $v_n=v_0^{(n)}.$