y^{''}-7y^'-8y=0,y(0)=1,y^'(0)=-1

Lösung

y^{^{''}} - 7 y^{^{'}} - 8 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

y = e^{- t}

Schritte zur Lösung

y^{''} (t) - 7 y^{'} (t) - 8 y = 0

Solve linear ODE:

y = e^{- t}

y = e^{- t}

y^{^{''''}} - 8 y^{^{'''}} + 18 y^{^{''}} - 27 y = 0

y^{^{''}} + y^{^{'}} = 0, y^{^{'}} (0) = 1

3 y^{^{''}} + 2 y^{^{'}} = 0, y (0) = - 6, y^{^{'}} (0) = - 18

\frac{3}{16} y^{^{''}} + 12 y = 0, y (0) = \frac{2}{3}, y^{^{'}} (0) = - 3

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (0) = 1, y^{^{'}} (0) = 3