(d^5-d)y=12e^x+8sin(x)-2x

Lösung

(d^{5} - d) y = 12 e^{x} + 8 sin (x) - 2 x

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + c_{4} cos (x) + c_{5} sin (x) + 3 x e^{x} + 2 x sin (x) + x^{2}

Schritte zur Lösung

(d^{5} - d) y = 12 e^{x} + 8 sin (x) - 2 x

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + c_{4} cos (x) + c_{5} sin (x) + 3 x e^{x} + 2 x sin (x) + x^{2}

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + c_{4} cos (x) + c_{5} sin (x) + 3 x e^{x} + 2 x sin (x) + x^{2}

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = e^{x} - x + 16

(d^{3} - 3 d + 2) \cdot y = 540 x^{3} \cdot e^{- x}

(d^{3} + 8) \cdot y = x^{4} + 2 x + 1 + 3 sin (x)

(d^{2} + d - 2) y = 1 + x - x^{2}

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