y^{''}-12y^'+37y=e^{6x}-x^2

解答

y^{^{''}} - 12 y^{^{'}} + 37 y = e^{6 x} - x^{2}

y = e^{6 x} (c_{1} cos (x) + c_{2} sin (x)) + e^{6 x} - \frac{x ^{2}}{37} - \frac{24 x}{1369} - \frac{214}{50653}

求解步骤

y^{''} (x) - 12 y^{'} (x) + 37 y = e^{6 x} - x^{2}

求解线性方程:

y = e^{6 x} (c_{1} cos (x) + c_{2} sin (x)) + e^{6 x} - \frac{x ^{2}}{37} - \frac{24 x}{1369} - \frac{214}{50653}

y = e^{6 x} (c_{1} cos (x) + c_{2} sin (x)) + e^{6 x} - \frac{x ^{2}}{37} - \frac{24 x}{1369} - \frac{214}{50653}

(D^{2} + 4 D + 3) y = 2 x e^{3 x} + 3 e^{3 x} cos (2 x)

y^{^{''''}} + 2 y^{^{''}} + y = cos (2 x) + 5

y^{^{''}} + 16 y = cos (4 t), y (0) = 1, y (0) = 0

y^{^{''}} + 4 y^{^{'}} + 20 x = 0

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 5 y = x^{3}