y^{''}+2y^'+y=0,y(0)=5,y(0)=-3

Lösung

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 5, y (0) = - 3

y = 5 e^{- t} + c_{2} t e^{- t}

Schritte zur Lösung

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

Solve linear ODE:

y = 5 e^{- t} + c_{2} t e^{- t}

y = 5 e^{- t} + c_{2} t e^{- t}

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

25 y^{^{''}} - 30 y^{^{'}} + 9 y = 0, y^{1} (0) = e^{3} \frac{x}{5}

4 y^{^{''}} - 4 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = - 1.5

(d^{4} - 16) y = 0

y^{^{''}} - \frac{2}{3} y^{^{'}} + \frac{1}{9} y = 0