(D^2+D+1)y=x^3

Lösung

(D^{2} + D + 1) y = x^{3}

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + x^{3} - 3 x^{2} + 6

Schritte zur Lösung

(D^{2} + D + 1) y = x^{3}

Solve linear ODE:

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + x^{3} - 3 x^{2} + 6

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + x^{3} - 3 x^{2} + 6

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

y^{^{''}} + 4 y = 5 x + 16

3 y^{^{''}} + y = cos (t)

y^{^{''}} - 4 y = 3 e - 2 t

- y^{^{''}} + y^{^{'}} = 1