(d^3-3d-2)y=x^3

Lösung

(d^{3} - 3 d - 2) y = x^{3}

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} x e^{- x} - \frac{x ^{3}}{2} + \frac{9 x ^{2}}{4} - \frac{27 x}{4} + \frac{69}{8}

Schritte zur Lösung

(d^{3} - 3 d - 2) y = x^{3}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} x e^{- x} - \frac{x ^{3}}{2} + \frac{9 x ^{2}}{4} - \frac{27 x}{4} + \frac{69}{8}

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} x e^{- x} - \frac{x ^{3}}{2} + \frac{9 x ^{2}}{4} - \frac{27 x}{4} + \frac{69}{8}

y^{^{''}} + y^{^{'}} - 2 y = 14 + 2 x - 2 x^{2}

y^{^{'''}} - y^{^{'}} = 4 e^{- x} + 3 e^{2} x

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

(d - 1)^{2} \cdot y = sin (x) \cdot x^{2} \cdot e^{x}

(d^{3} + 1) \cdot y = cos (2 x - 1)