(d^2x)/(dt^2)-(dx)/(dt)-2x=4t

解答

\frac{d ^{2} x}{d t ^{2}} - \frac{d x}{d t} - 2 x = 4 t

x = c_{1} e^{2 t} + c_{2} e^{- t} - 2 t + 1

求解步骤

\frac{d ^{2} x}{d t ^{2}} - \frac{d x}{d t} - 2 x = 4 t

求解线性方程:

x = c_{1} e^{2 t} + c_{2} e^{- t} - 2 t + 1

x = c_{1} e^{2 t} + c_{2} e^{- t} - 2 t + 1

x^{^{''}} + 2 x + 5 x = 1, x^{^{'}} (0) = 0, x (0) = 0

(d^{2} - 4 d + 4) y = x^{2} + e^{x} + cos (2 x)

y^{^{''}} + y^{^{'}} - 6 y = - e^{2 x} + 12 x^{2} + 2 x + 3

y^{^{''}} + 6 y^{^{'}} + 25 x = 0

y^{^{''}} - n^{2} y = \frac{2 cos ( πn ) x}{n}