(D^6+6D^4+9D^2)y=0

Lösung

(D^{6} + 6 D^{4} + 9 D^{2}) y = 0

y = c_{1} + c_{2} x + c_{3} cos (3 x) + c_{4} sin (3 x) + x (c_{5} cos (3 x) + c_{6} sin (3 x))

Schritte zur Lösung

(D^{6} + 6 D^{4} + 9 D^{2}) y = 0

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} cos (3 x) + c_{4} sin (3 x) + x (c_{5} cos (3 x) + c_{6} sin (3 x))

y = c_{1} + c_{2} x + c_{3} cos (3 x) + c_{4} sin (3 x) + x (c_{5} cos (3 x) + c_{6} sin (3 x))

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = 5

x^{^{'''}} - x^{^{''}} = 0, x (0) = 1, x^{^{'}} (0) = 3, x^{^{''}} (0) = 2

y^{^{''}} - 10 y^{^{'}} + 34 y = 0, y (0) = 5, y^{^{'}} (0) = - 2

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

4 y^{^{''}} + 28 y = 0, y (0) = 3, y^{^{'}} (0) = 7