y^{''}+3y^'+2y=6e^t,y(0)=1,y^'(0)=2

Lösung

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{t}, y (0) = 1, y^{^{'}} (0) = 2

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

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) + 2 y = 6 e^{t}

Solve linear ODE:

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

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

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 15 t

y^{^{''}} + 9 y = e^{x}

y^{^{''''}} + 8 y^{^{''}} + 16 y = 48 + cos (4 t)

y^{^{''}} + 16 y = 32 t

y^{^{''}} + 2 y^{^{'}} + 5 y = 24 e^{- t} cos (2 t)