Chemical Reactions 1

Problem 1.

The functions $x(t)$ and $y(t)$ describe the concentration of two substances, respectively. The first component transforms into the second one with the rate coefficient $k\gt 0$, and the second component decomposes at the rate $\mu\gt 0$. Describe the system.

Chemical Reactions 2

Problem 2.

The functions $u(t)$ and $v(t)$ describe the concentration of two substances, respectively. The components transform into each other with the rate coefficient $k\gt 0$, and the following system describes the process \begin{align*} u'(t)&=ku(t)v(t),\\ v'(t)&=-ku(t)v(t). \end{align*} For the sake of simplicity let $k:=1$, and $u(0),v(0)=1$. Approximate the solutions by 3rd order polynomials.