(D^2+5D+6)y=x^2+2x

Lösung

(D^{2} + 5 D + 6) y = x^{2} + 2 x

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} + \frac{x}{18} - \frac{11}{108}

Schritte zur Lösung

(D^{2} + 5 D + 6) y = x^{2} + 2 x

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} + \frac{x}{18} - \frac{11}{108}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{x ^{2}}{6} + \frac{x}{18} - \frac{11}{108}

490 y^{^{''}} + 20 y = 8 cos (6 t)

\frac{d ^{2} y}{d x ^{2}} - 4 y = \frac{e ^{2 x}}{x}

2 y^{^{''}} + 3 y^{^{'}} + 3 = cos (x)

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 4 + 6 sin (x)

y^{^{''}} + 6 y^{^{'}} + 9 y = - 4 x e^{- 2 x} + 2 e^{- 3 x} + 3