(D^2-D-2)y=18xe^{-x}

Lösung

(D^{2} - D - 2) y = 18 x e^{- x}

y = c_{1} e^{2 x} + c_{2} e^{- x} - 3 x^{2} e^{- x} - 2 e^{- x} x

Schritte zur Lösung

(D^{2} - D - 2) y = 18 x e^{- x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} - 3 x^{2} e^{- x} - 2 e^{- x} x

y = c_{1} e^{2 x} + c_{2} e^{- x} - 3 x^{2} e^{- x} - 2 e^{- x} x

y^{^{''}} - 2 y^{^{'}} + y = e^{t}, y (0) = 1, y^{^{'}} (0) = 0

x^{^{''}} + x = 1

x^{^{''}} + x = 5

y^{^{'''}} + y^{^{''}} - 1 = 0

y^{^{''}} + y^{^{'}} = t, y (0) = 1, y^{^{'}} (0) = 2