(4D^5-15D^3-5D^2+15D+9)y=0

Lösung

(4 D^{5} - 15 D^{3} - 5 D^{2} + 15 D + 9) y = 0

y = c_{1} e^{- x} + c_{2} x e^{- x} + c_{3} x^{2} e^{- x} + c_{4} e^{\frac{3 x}{2}} + c_{5} e^{\frac{3 x}{2}} x

Schritte zur Lösung

(4 D^{5} - 15 D^{3} - 5 D^{2} + 15 D + 9) y = 0

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} + c_{3} x^{2} e^{- x} + c_{4} e^{\frac{3 x}{2}} + c_{5} e^{\frac{3 x}{2}} x

y = c_{1} e^{- x} + c_{2} x e^{- x} + c_{3} x^{2} e^{- x} + c_{4} e^{\frac{3 x}{2}} + c_{5} e^{\frac{3 x}{2}} x

f^{^{''}} (x) = 6 f^{^{'}} (x) - 6 f (x)

16 y^{^{''}} + 64 y = 0, y (0) = 0.3, y^{^{'}} (0) = - 0.2

y^{^{'''}} - y^{^{''}} - 9 y^{^{'}} + 9 y = 0

y^{^{''}} - 5 y + 6 y = 0

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 8 y = 0