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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

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

(d^{3} - 6 d^{2} + 11 d - 6) \cdot y = 0

y^{^{''}} - 7 y^{^{'}} + 15 y = 0

y^{^{''}} + 4 y^{^{'}} + 2.5 y = 0