x^{''}+x^'+1/3 x=0,x(0)=4,x^'(0)=0

解答

x^{^{''}} + x^{^{'}} + \frac{1}{3} x = 0, x (0) = 4, x^{^{'}} (0) = 0

x = e^{- \frac{t}{2}} (4 cos (\frac{t}{2 3}) + 43 sin (\frac{t}{2 3}))

求解步骤

x^{''} (t) + x^{'} (t) + \frac{1}{3} x = 0

求解线性方程:

x = e^{- \frac{t}{2}} (4 cos (\frac{t}{2 3}) + 43 sin (\frac{t}{2 3}))

x = e^{- \frac{t}{2}} (4 cos (\frac{t}{2 3}) + 43 sin (\frac{t}{2 3}))

y^{^{'''}} + 3 y^{^{''}} - 10 y^{^{'}} = 0

81 y^{^{''}} - 18 y^{^{'}} + 5 y = 0, y (1) = 1, y^{^{'}} (1) = 7

9 x^{^{''}} + 9 x^{^{'}} - 4 x = 0

y^{^{''}} + y = 0, y (π) = 1, y (0) = 1

a \cdot y^{^{''}} + b \cdot y = 0