(4D^4-4D^3-23D^2+12D+36)y=0

Lösung

(4 D^{4} - 4 D^{3} - 23 D^{2} + 12 D + 36) y = 0

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

Schritte zur Lösung

(4 D^{4} - 4 D^{3} - 23 D^{2} + 12 D + 36) y = 0

Solve linear ODE:

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

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

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

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