t_{2}=frac{ln(frac{x_{m}}{x_{0}}-1)+(31)}{r_{0}} lösen

$$t _ { 2 } = \frac { \ln ( \frac { x _ { m } } { x _ { 0 } } - 1 ) + ( 31 ) } { r _ { 0 } }$$

Nach r_0 auflösen (komplexe Lösung)

$$\left\{\begin{matrix}r_{0}=\frac{\ln(\frac{x_{m}-x_{0}}{x_{0}})+31}{t_{2}}\text{, }&x_{m}\neq \frac{x_{0}}{e^{31}}+x_{0}\text{ and }t_{2}\neq 0\text{ and }x_{m}\neq x_{0}\text{ and }x_{0}\neq 0\\r_{0}\neq 0\text{, }&t_{2}=0\text{ and }x_{0}=\frac{e^{31}x_{m}}{e^{31}+1}\text{ and }x_{m}\neq 0\end{matrix}\right,$$

Nach t_2 auflösen (komplexe Lösung)

$$t_{2}=\frac{\ln(\frac{x_{m}-x_{0}}{x_{0}})+31}{r_{0}}$$

$$r_{0}\neq 0\text{ and }x_{m}\neq x_{0}\text{ and }x_{0}\neq 0$$

Nach r_0 auflösen

$$\left\{\begin{matrix}r_{0}=\frac{\ln(\frac{x_{m}-x_{0}}{x_{0}})+31}{t_{2}}\text{, }&x_{m}\neq \frac{x_{0}}{e^{31}}+x_{0}\text{ and }t_{2}\neq 0\text{ and }x_{m}\neq x_{0}\text{ and }\left(x_{m}<x_{0}\text{ or }x_{0}>0\right)\text{ and }\left(x_{0}<0\text{ or }x_{m}>x_{0}\right)\text{ and }x_{0}\neq 0\\r_{0}\neq 0\text{, }&t_{2}=0\text{ and }x_{0}=\frac{e^{31}x_{m}}{e^{31}+1}\text{ and }x_{m}\neq 0\end{matrix}\right,$$

Nach t_2 auflösen

$$t_{2}=\frac{\ln(\frac{x_{m}-x_{0}}{x_{0}})+31}{r_{0}}$$

$$\left(r_{0}\neq 0\text{ and }x_{m}<x_{0}\text{ and }x_{0}<0\right)\text{ or }\left(r_{0}\neq 0\text{ and }x_{m}>x_{0}\text{ and }x_{0}>0\right)$$