Nagekomen bericht:-)

\( \begin{array}{l} y'' - y' - 2y = 0 \\ y( - 1) = 1 \\ y(1) = 0 \\ k^2 - k - 2 = 0 \\ (k - 2)(k + 1) = 0 \\ k = 2 \vee k = - 1 \\ y = C_1 \cdot e^{2x} + C_2 \cdot e^{ - x} \\ \left\{ \begin{array}{l} C_1 \cdot e^{ - 2} + C_2 \cdot e = 1 \\ C_1 \cdot e^2 + C_2 \cdot e^{ - 1} = 0 \\ \end{array} \right. \\ \left\{ \begin{array}{l} C_1 = \frac{{e^2 }}{{1 - e^6 }} \\ C_2 = \frac{{e^5 }}{{e^6 - 1}} \\ \end{array} \right. \\ y = \frac{{e^2 }}{{1 - e^6 }} \cdot e^{2x} + \frac{{e^5 }}{{e^6 - 1}} \cdot e^{ - x} \\ y = - \frac{{e^2 }}{{e^6 - 1}} \cdot e^{2x} + \frac{{e^5 }}{{e^6 - 1}} \cdot e^{ - x} \\ y = \frac{{e^{5 - x} - e^{2x + 2} }}{{e^6 - 1}} \\ \end{array} \)