(d^2-2d+5)^2y=0

Lösung

(d^{2} - 2 d + 5)^{2} y = 0

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

Schritte zur Lösung

(d^{2} - 2 d + 5)^{2} y = 0

Solve linear ODE:

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

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

3 x y^{^{'}} = 3 x y^{^{''}}

36 y^{^{''}} - 81 y = 0, y (0) = 0, y^{^{'}} (0) = 1

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

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y^{^{'}} (\frac{π}{2}) = 12

y^{^{''}} + 6 y^{^{'}} + 2 y = 0, y (0) = 4, y^{^{'}} (0) = 0