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

Lösung

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

y = \frac{1}{3} e^{- t} - \frac{1}{3} e^{- 4 t}

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = \frac{1}{3} e^{- t} - \frac{1}{3} e^{- 4 t}

y = \frac{1}{3} e^{- t} - \frac{1}{3} e^{- 4 t}

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

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 4, y^{^{'}} (0) = 16

(D^{2} + 9) y = 0, Dy = 0, y = 2, x = 30