(d^3x)/(dt^3)-x=0

解答

\frac{d ^{3} x}{d t ^{3}} - x = 0

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

求解步骤

\frac{d ^{3} x}{d t ^{3}} - x = 0

求解线性方程:

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

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

l in e a r x^{^{''}} + 16 x = 0, x^{^{'}} (0) = 5

l in e a r y^{^{'''}} - 3 y^{^{''}} + 2 y^{^{'}} = 0

y^{^{''''}} - 6 y^{^{'''}} + 17 y^{^{''}} - 28 y^{^{'}} + 20 y = 0

y^{^{''}} + 9 y = 0, y (0) = 6, y^{^{'}} (0) = - 4

y^{^{''}} - 3 y^{^{'}} - 5 y = 0, y (0) = - 2, y^{^{'}} (0) = 2