(D^2-3D+2)y=6e^{3x}+sin(2x)

解答

(D^{2} - 3 D + 2) y = 6 e^{3 x} + sin (2 x)

y = c_{1} e^{2 x} + c_{2} e^{x} + 3 e^{3 x} - \frac{1}{20} sin (2 x) + \frac{3}{20} cos (2 x)

求解步骤

(D^{2} - 3 D + 2) y = 6 e^{3 x} + sin (2 x)

求解线性方程:

y = c_{1} e^{2 x} + c_{2} e^{x} + 3 e^{3 x} - \frac{1}{20} sin (2 x) + \frac{3}{20} cos (2 x)

y = c_{1} e^{2 x} + c_{2} e^{x} + 3 e^{3 x} - \frac{1}{20} sin (2 x) + \frac{3}{20} cos (2 x)

y^{^{''}} + 18 y^{^{'}} + 81 y = x

y^{^{''}} + 81 y = 2 sin (a t)

y^{^{''}} + 19 y = 4 e^{x}

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

y^{^{''}} - y^{^{'}} = 8 e^{x}