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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 3 y = 0, y (0) = 0, y^{^{'}} (0) = 1

60 x^{^{''}} + 240 x = 0

y^{^{''}} + (\frac{1}{2}) y = 0

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

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 8, y^{^{'}} (0) = 7