(D^4+D^2)y=3x^2+4sin(x)-2cos(x)

解答

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

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

求解步骤

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

求解线性方程:

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

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

y^{^{''}} + 2 y = - 18 x e^{2 x}

y^{^{''}} - y^{^{'}} - 6 y = 2 cos (x) - 2 e^{3 x} + 10

y^{^{''}} + 5 y^{^{'}} + 6 y = x e^{- 2 x}

\frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 6 x = 5 e^{- t}

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + x = 3 cos (t)