(D^3-3D^2+4D-2)y=cos(x)

Lösung

(D^{3} - 3 D^{2} + 4 D - 2) y = cos (x)

y = c_{1} e^{x} + e^{x} (c_{2} cos (x) + c_{3} sin (x)) + \frac{3}{10} sin (x) + \frac{1}{10} cos (x)

Schritte zur Lösung

(D^{3} - 3 D^{2} + 4 D - 2) y = cos (x)

Solve linear ODE:

y = c_{1} e^{x} + e^{x} (c_{2} cos (x) + c_{3} sin (x)) + \frac{3}{10} sin (x) + \frac{1}{10} cos (x)

y = c_{1} e^{x} + e^{x} (c_{2} cos (x) + c_{3} sin (x)) + \frac{3}{10} sin (x) + \frac{1}{10} cos (x)

y^{^{''}} + 5 y^{^{'}} = 100 sin (5 t) + 150 cos (5 t)

y^{^{''}} + 49 y = - 5 cos (7 t + π^{3})

y^{^{''}} + b^{2} y = sin (b t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{'''}} - y^{^{'}} = 6 sin (t)

y^{^{''}} + 4 y^{^{'}} + 5 y = (e^{- 2 x}) sec (x)