(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} x e^{- 3 x} + c_{3} e^{3 x} + c_{4} x e^{3 x} + c_{5} cos (2 x) + c_{6} sin (2 x) + x (c_{7} cos (2 x) + c_{8} sin (2 x)) + x^{2} (c_{9} cos (2 x) + c_{10} 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} x e^{- 3 x} + c_{3} e^{3 x} + c_{4} x e^{3 x} + c_{5} cos (2 x) + c_{6} sin (2 x) + x (c_{7} cos (2 x) + c_{8} sin (2 x)) + x^{2} (c_{9} cos (2 x) + c_{10} sin (2 x))

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} + c_{3} e^{3 x} + c_{4} x e^{3 x} + c_{5} cos (2 x) + c_{6} sin (2 x) + x (c_{7} cos (2 x) + c_{8} sin (2 x)) + x^{2} (c_{9} cos (2 x) + c_{10} sin (2 x))

(D^{2} + 1)^{3} y = 0

y^{^{''}} - y^{^{'}} - 12 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

y^{^{'''}} + 7 y^{^{''}} + 15 y^{^{'}} + 9 y = 0

4 y^{^{''}} + 3 y^{^{'}} = 0

\frac{d ^{3} y}{d x ^{3}} - 3 \frac{d ^{2} y}{d x ^{2}} + 4 y = 0