y^{'''}-5y^{''}+6y^'=5+4sin(x)

解答

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 5 + 4 sin (x)

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{3 x} + \frac{5 x}{6} + \frac{2}{5} sin (x) - \frac{2}{5} cos (x)

求解步骤

y^{'''} (x) - 5 y^{''} (x) + 6 y^{'} (x) = 5 + 4 sin (x)

求解线性方程:

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{3 x} + \frac{5 x}{6} + \frac{2}{5} sin (x) - \frac{2}{5} cos (x)

y = c_{1} + c_{2} e^{2 x} + c_{3} e^{3 x} + \frac{5 x}{6} + \frac{2}{5} sin (x) - \frac{2}{5} cos (x)

y^{^{''}} + 2 y^{^{'}} - 4 y = 8 x^{2}

8 y^{^{''}} - 32 y = 16 cos (x)

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = 6 e^{2 x}

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

y^{^{''}} + 9 y = cos (3 t), y (0) = 2, y^{^{'}} (0) = 5