(D^2+2)3(D^2-3)2y=0

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 5, y^{^{'}} (0) = 12

25 y + 8 y^{^{'}} + y^{^{''}} = 0

\frac{4}{32} y^{^{''}} + 3 y^{^{'}} = 0

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

c \frac{d ^{2} y}{d x ^{2}} = y