y^{''}-y^'-2y=0,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = (1 - \frac{2}{3}) e^{2 t} + \frac{2}{3} e^{- t}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 2 y = 0

Solve linear ODE:

y = (1 - \frac{2}{3}) e^{2 t} + \frac{2}{3} e^{- t}

y = (1 - \frac{2}{3}) e^{2 t} + \frac{2}{3} e^{- t}

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

2 y^{^{''}} + 2 y^{^{'}} + 3 y = 0

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 15, y^{^{'}} (0) = - 6

y^{^{''}} + y = 0, y^{^{'}} (\frac{π}{2}) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} - 2 y = 0