y^{''}+2y^'+y=0,y(0)=10,y^'(0)=-9

Lösung

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 10, y^{^{'}} (0) = - 9

y = 10 e^{- t} + e^{- t} t

Schritte zur Lösung

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

Solve linear ODE:

y = 10 e^{- t} + e^{- t} t

y = 10 e^{- t} + e^{- t} t

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

y^{^{''}} - 4 y^{^{'}} - 4 y = 0, y (0) = 2, y^{^{'}} (0) = 16

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 3, y (0) = - 12

(D^{5} - 6 D^{4} + 9 D^{3}) y = 0

y^{^{''}} + 4 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0