y^{'''}-4y^{''}+y^'+6y=3e^{4t}

解答

y^{^{'''}} - 4 y^{^{''}} + y^{^{'}} + 6 y = 3 e^{4 t}

y = c_{1} e^{- t} + c_{2} e^{2 t} + c_{3} e^{3 t} + \frac{3}{10} e^{4 t}

求解步骤

y^{'''} (t) - 4 y^{''} (t) + y^{'} (t) + 6 y = 3 e^{4 t}

求解线性方程:

y = c_{1} e^{- t} + c_{2} e^{2 t} + c_{3} e^{3 t} + \frac{3}{10} e^{4 t}

y = c_{1} e^{- t} + c_{2} e^{2 t} + c_{3} e^{3 t} + \frac{3}{10} e^{4 t}

y^{^{''}} + 4 y = sin (t) - H (t - 2 π) sin (t - 2 π)

y^{^{''}} + y = sin (a t)

y^{^{''}} - 4 y^{^{'}} + 13 y = 24 e^{2 x} cos (3 x)

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

y^{^{''}} + 5 y^{^{'}} + 4 y = t e^{- t} H (t)