(4D^2+4D+1)y=xe^{-x/2}sin(x)

Lösung

(4 D^{2} + 4 D + 1) y = x e^{- \frac{x}{2}} sin (x)

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

Schritte zur Lösung

(4 D^{2} + 4 D + 1) y = x e^{- \frac{x}{2}} sin (x)

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 4 y = 111 e^{2 x} cos (3 x)

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

y^{^{''}} + 9 y = 5 sin (2 x), y (0) = 1, y^{^{'}} (0) = 0

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

x^{^{''}} + 2 x^{^{'}} + x = t