y^{''}-y^'-2y=e^{-2t}-3e^{-t}

解答

y^{^{''}} - y^{^{'}} - 2 y = e^{- 2 t} - 3 e^{- t}

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{4} e^{- 2 t} + e^{- t} t

求解步骤

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

求解线性方程:

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{4} e^{- 2 t} + e^{- t} t

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{4} e^{- 2 t} + e^{- t} t

y^{^{''}} - 2 y^{^{'}} + 2 y - 3 cos (x) = e^{x}

y^{^{'''}} + 6 y^{^{''}} = 3 - cos (x)

x^{^{''}} + 3 x^{^{'}} + \frac{61}{4} x = \frac{1}{2} e^{t}

y^{^{''}} + 4 y^{^{'}} = 3 sin (2 t)

y^{^{'''}} + y^{^{'}} = sec (t), y^{^{'}} (0) = 3