(d^4-i^2)y=0

解答

(d^{4} - i^{2}) y = 0

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

求解步骤

(d^{4} - i^{2}) y (y) = 0

求解线性方程:

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

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

(d^{3} - d^{2} + 2 d - d) y = 0

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 0

(d^{3} + d^{2} + d) \cdot y = 0

(d^{3} + d^{2} + d) y = 0

(d^{3} - 2 d^{2} - 5 d + 6) y = 0