y^{''}+4y^'+5y=(e^{-2x})sec(x)

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = (e^{- 2 x}) sec (x)

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

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = (e^{- 2 x}) sec (x)

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 4 y = x e^{2 x} + 1

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

y^{^{''}} - 2 y^{^{'}} + y = (\frac{e}{x})^{x}

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

y^{^{'''}} + 6 y^{^{''}} + 12 y^{^{'}} + 8 y = 9 e^{- 2 x}