(2D^5-7D^4+12D^3+8D^2)y=0

Lösung

(2 D^{5} - 7 D^{4} + 12 D^{3} + 8 D^{2}) y = 0

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

Schritte zur Lösung

(2 D^{5} - 7 D^{4} + 12 D^{3} + 8 D^{2}) y = 0

Solve linear ODE:

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

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

y^{^{''}} + 22 y^{^{'}} + 2 y = 0

y^{^{''}} + 4 y^{^{'}} + 29 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y (0) = 2, y^{^{'}} (0) = 10

\frac{d ^{4} y}{d x ^{4}} + 6 \frac{d ^{2} y}{d x ^{2}} + 9 y = 0

9 y^{^{'''}} + 12 y^{^{''}} + 4 y^{^{'}} = 0