Problem
\( y^{\prime \prime}-y^{\prime}-y=0 \)
Solution
Step 1 ：\( m^2 - m - 1 = 0 \)
Step 2 ：\( m = \frac{1 \pm \sqrt{5}}{2} \)
Step 3 ：\( y(x) = C_1e^{\frac{1 + \sqrt{5}}{2}x} + C_2e^{\frac{1 - \sqrt{5}}{2}x} \)
Step 1 ：\( m^2 - m - 1 = 0 \)
Step 2 ：\( m = \frac{1 \pm \sqrt{5}}{2} \)
Step 3 ：\( y(x) = C_1e^{\frac{1 + \sqrt{5}}{2}x} + C_2e^{\frac{1 - \sqrt{5}}{2}x} \)
