(6D^2+4D+2)y=xe^{-2x}

Lösung

(6 D^{2} + 4 D + 2) y = x e^{- 2 x}

y = e^{- \frac{x}{3}} (c_{1} cos (\frac{2 x}{3}) + c_{2} sin (\frac{2 x}{3})) + \frac{e ^{- 2 x} x}{18} + \frac{5}{81} e^{- 2 x}

Schritte zur Lösung

(6 D^{2} + 4 D + 2) y = x e^{- 2 x}

Solve linear ODE:

y = e^{- \frac{x}{3}} (c_{1} cos (\frac{2 x}{3}) + c_{2} sin (\frac{2 x}{3})) + \frac{e ^{- 2 x} x}{18} + \frac{5}{81} e^{- 2 x}

y = e^{- \frac{x}{3}} (c_{1} cos (\frac{2 x}{3}) + c_{2} sin (\frac{2 x}{3})) + \frac{e ^{- 2 x} x}{18} + \frac{5}{81} e^{- 2 x}

- 21 y + 4 y^{^{'}} + y^{^{''}} = t + 1

so l v e f or y, d (y) = 7 (2)^{y}

y^{^{''}} + 4 y^{^{'}} + 5 y = 1 - 5 x + 8 (cos (x) - sin (x))

4 x^{^{''}} - 4 x^{^{'}} + x = \frac{8}{t ^{2}} e^{\frac{t}{2}}

- y^{^{''}} + 2 y^{^{'}} + 3 y = 1