y^{''}+2y^'+y=1-\H(t-1)

Lösung

y^{^{''}} + 2 y^{^{'}} + y = 1 - H (t - 1)

y = c_{1} e^{- t} + c_{2} t e^{- t} + e^{- t} \cdot \int - e^{t} t (1 - H (t - 1)) d t + e^{- t} t \cdot \int e^{t} (1 - H (t - 1)) d t

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + y = 1 - H (t - 1)

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} t e^{- t} + e^{- t} \cdot \int - e^{t} t (1 - H (t - 1)) d t + e^{- t} t \cdot \int e^{t} (1 - H (t - 1)) d t

y = c_{1} e^{- t} + c_{2} t e^{- t} + e^{- t} \cdot \int - e^{t} t (1 - H (t - 1)) d t + e^{- t} t \cdot \int e^{t} (1 - H (t - 1)) d t

y^{^{''}} + 4 y = 8 t^{2}

y^{^{''}} - y = sin (x) + e^{x}

y^{^{''}} + y = t^{2}

5 y^{^{''}} + 6 y^{^{'}} + 80 y = - 24 sin (4 t)

y^{^{''}} - y^{^{'}} - 2 y = e^{- x}