y^{''}+y=e^{-x}(2sin(x)+4cos(x))

Lösung

y^{^{''}} + y = e^{- x} (2 sin (x) + 4 cos (x))

y = c_{1} cos (x) + c_{2} sin (x) - \frac{6}{5} e^{- x} sin (x) + \frac{8}{5} e^{- x} cos (x)

Schritte zur Lösung

y^{''} (x) + y = e^{- x} (2 sin (x) + 4 cos (x))

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - \frac{6}{5} e^{- x} sin (x) + \frac{8}{5} e^{- x} cos (x)

y = c_{1} cos (x) + c_{2} sin (x) - \frac{6}{5} e^{- x} sin (x) + \frac{8}{5} e^{- x} cos (x)

y^{^{''}} + y^{^{'}} - 7 y = 3 e^{2 x} - 2 e^{3 x}

y^{^{'''}} + y^{^{'}} - 10 = x e^{2 x}

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

y^{^{''}} + y^{^{'}} - 2 y = 18 x e^{- 2 x} - 12 e^{- 2 x}

y^{^{''}} + 5 y^{^{'}} + 4 y = 10 x e^{5 x}