I think that the solution of the diffrential equation :
$$
\frac{\mathrm{d}x}{\mathrm{d}t} = -kx\quad \text{with}\quad x(t=0)=1\quad \text{and}\quad x\in\left[0, 1\right].
$$
has to be :
$$
x(t) = \mathrm{exp}\left(-kt\right).
$$
not
$$
x(t) = \mathrm{exp}\left(-kx\right).
$$
since the solution has to be a function of time t.
Dear @SoufianeAitlhadj,
many thanks for your comment and apologies for the delayed reply. You are correct. Good job spotting this typo. I'll note this change for the next revision.
Best, Andre
I think that the solution of the diffrential equation : $$ \frac{\mathrm{d}x}{\mathrm{d}t} = -kx\quad \text{with}\quad x(t=0)=1\quad \text{and}\quad x\in\left[0, 1\right]. $$ has to be : $$ x(t) = \mathrm{exp}\left(-kt\right). $$ not $$ x(t) = \mathrm{exp}\left(-kx\right). $$ since the solution has to be a function of time t.