y^{'''}+3y^{''}+y^'+3y=e^x+4

解答

y^{^{'''}} + 3 y^{^{''}} + y^{^{'}} + 3 y = e^{x} + 4

y = c_{1} e^{- 3 x} + c_{2} cos (x) + c_{3} sin (x) + \frac{1}{8} e^{x} + \frac{4}{3}

求解步骤

y^{'''} (x) + 3 y^{''} (x) + y^{'} (x) + 3 y = e^{x} + 4

求解线性方程:

y = c_{1} e^{- 3 x} + c_{2} cos (x) + c_{3} sin (x) + \frac{1}{8} e^{x} + \frac{4}{3}

y = c_{1} e^{- 3 x} + c_{2} cos (x) + c_{3} sin (x) + \frac{1}{8} e^{x} + \frac{4}{3}

y^{^{''}} + 9 y = cos (2 x)

y^{^{''}} - 10 y^{^{'}} + 25 y = x

\frac{d ^{2} y}{d x ^{2}} + y = x sin (x)

\frac{1}{6} y^{^{''}} + 6 y = tan (6 t) - \frac{1}{2} e^{2 t}

9 y^{^{''}} - y = x e^{\frac{x}{3}}, y (0) = 1, y (0) = 0