y^{''}+8y^'+15y=0,y(0)=0,y^'(0)=1

Lösung

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y = \frac{1}{2} e^{- 3 t} - \frac{1}{2} e^{- 5 t}

Schritte zur Lösung

y^{''} (t) + 8 y^{'} (t) + 15 y = 0

Solve linear ODE:

y = \frac{1}{2} e^{- 3 t} - \frac{1}{2} e^{- 5 t}

y = \frac{1}{2} e^{- 3 t} - \frac{1}{2} e^{- 5 t}

y^{^{''}} - 6 y^{^{'}} + 5 y = 0, y (0) = 3, y^{^{'}} (0) = 1

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

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 0

2 y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0