x^{''}+x^'=e^{-t}

解答

x^{^{''}} + x^{^{'}} = e^{- t}

x = c_{1} + c_{2} e^{- t} - e^{- t} t

求解步骤

x^{''} (t) + x^{'} (t) = e^{- t}

求解线性方程:

x = c_{1} + c_{2} e^{- t} - e^{- t} t

x = c_{1} + c_{2} e^{- t} - e^{- t} t

y^{^{''}} + 49 y = 8 cos (7 x) (3 x + 2)

y^{^{''}} + y^{^{'}} - 6 y = t - 2 π, y (0) = 1, y^{^{'}} (0) = 2

- v y^{^{''}} - a y = c

y^{^{''}} - 7 y^{^{'}} + 10 y = e^{3 x} (- 1 + 10 x)

y^{^{''}} - 9 y^{^{'}} + 18 y = e^{6 t}