(D^4-2D^2+1)y=cos(x)

Lösung

(D^{4} - 2 D^{2} + 1) y = cos (x)

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

Schritte zur Lösung

(D^{4} - 2 D^{2} + 1) y = cos (x)

Solve linear ODE:

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

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

y^{^{''}} + 5 y^{^{'}} + 4 y = 2 x e^{2 x}

y^{^{''}} + y = 4 x e^{x}

y^{^{''}} + 16 y = 16 sin (4 t)

y^{^{''}} - 7 y^{^{'}} + 6 y = x

y^{^{''}} - 2 y^{^{'}} + 3 = 0