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} + 2 t e^{- t}

Schritte zur Lösung

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

Solve linear ODE:

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

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

5 y^{^{''}} + 2 y^{^{'}} + 7 y = 0

3 y^{^{''}} + 8 y^{^{'}} + 3 y = 0

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

6 y^{^{''}} + 17 y^{^{'}} - 3 y = 0

y^{^{''}} - 15 y^{^{'}} + 56 y = 0