4y^{''}-y^'-y=0

Lösung

4 y^{^{''}} - y^{^{'}} - y = 0

y = c_{1} e^{\frac{( 1 + 17 ) t}{8}} + c_{2} e^{\frac{( 1 - 17 ) t}{8}}

Schritte zur Lösung

4 y^{''} (t) - y^{'} (t) - y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 1 + 17 ) t}{8}} + c_{2} e^{\frac{( 1 - 17 ) t}{8}}

y = c_{1} e^{\frac{( 1 + 17 ) t}{8}} + c_{2} e^{\frac{( 1 - 17 ) t}{8}}

\frac{1}{8} y^{^{''}} + 16 y = 0

y^{^{''''}} - 4 y = 0

y^{^{''}} = 6 y^{^{'}} - 8 y

y^{^{''}} + \frac{64}{17} \cdot y^{^{'}} + \frac{320}{17} \cdot y = 0

6 y^{^{''}} - y^{^{'}} - y = 0, y (0) = 1.25