y^{''}+8y^'+16y=0,y(0)=5,y^'(0)=0

Lösung

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y = 5 e^{- 4 t} + 20 t e^{- 4 t}

Schritte zur Lösung

y^{''} (t) + 8 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = 5 e^{- 4 t} + 20 t e^{- 4 t}

y = 5 e^{- 4 t} + 20 t e^{- 4 t}

(y^{^{''''}} + 8 y^{^{''}} + 16 y)^{2} = 0

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} - 4 y = 0, y^{0} = 0, y^{^{'}} 0 = 1