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

Lösung

y^{^{''}} + 6 y^{^{'}} + 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

y^{''} (x) + 6 y^{'} (x) + 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^{^{'}} = 30 e^{- 3 t}

y^{^{''}} - 2 y^{^{'}} + y = 5 x e^{x} sin (x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 + e^{2 t}

y^{^{''}} + 12 y^{^{'}} + 37 y = 4 H (t)

y^{^{''}} - y^{^{'}} + 441 y = 21 sin (21 t)