x^{''}+7x^'+6x=sin(2t)

解答

x^{^{''}} + 7 x^{^{'}} + 6 x = sin (2 t)

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{1}{100} sin (2 t) - \frac{7}{100} cos (2 t)

求解步骤

x^{''} (t) + 7 x^{'} (t) + 6 x = sin (2 t)

求解线性方程:

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{1}{100} sin (2 t) - \frac{7}{100} cos (2 t)

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + \frac{1}{100} sin (2 t) - \frac{7}{100} cos (2 t)

y^{^{''}} + 2 y = cos (8 t)

y^{^{'''}} + y^{^{''}} = 2^{x}

y^{^{''}} - y^{^{'}} - y = x^{3}

y^{^{''}} + 9 y = sin (x) + cos (x)

y^{^{''}} + 2 y^{^{'}} + y = sec^{2} (x)