(D^2+6D+9)y=(16e^{-3x})/(x^2+1)

Lösung

(D^{2} + 6 D + 9) y = \frac{16 e ^{- 3 x}}{x ^{2} + 1}

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} - 8 e^{- 3 x} ln (x^{2} + 1) + 16 e^{- 3 x} x arctan (x)

Schritte zur Lösung

(D^{2} + 6 D + 9) y = \frac{16 e ^{- 3 x}}{x ^{2} + 1}

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} - 8 e^{- 3 x} ln (x^{2} + 1) + 16 e^{- 3 x} x arctan (x)

y = c_{1} e^{- 3 x} + c_{2} x e^{- 3 x} - 8 e^{- 3 x} ln (x^{2} + 1) + 16 e^{- 3 x} x arctan (x)

y^{^{''}} + 2 y^{^{'}} + 2 y = 5 sin (t) + 5 cos (t)

2 y^{^{''}} - 3 y^{^{'}} = 9 x^{2} + 10

y^{^{''}} - y^{^{'}} - 2 y = sin (t)

y^{^{''}} + 4 y = sin (x), y (0) = 1, y^{^{'}} (0) = 2

x^{^{''}} + 4 x = 289 + e^{t} \cdot sin (2 t)