(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)

(d^{4} - 1) y = sin (x)

(d^{2} - 3 d + 2) y = x \cdot e^{x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 12 e^{2 x} + x^{2}

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

(d^{4} - 2 d^{2} + 1) \cdot y = cos (x)