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

Lösung

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

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{( - 8 e - 1 ) x}{2} + \frac{4 e - 1}{4}

Schritte zur Lösung

y^{'''} (x) - 2 y^{''} (x) - y^{'} (x) + 2 y = - 8 e x + 6 e - x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{( - 8 e - 1 ) x}{2} + \frac{4 e - 1}{4}

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} e^{x} + \frac{( - 8 e - 1 ) x}{2} + \frac{4 e - 1}{4}

y^{^{''}} + 16 y = csc (4 x)

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

y^{^{''}} - y^{^{'}} = - 9

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

(D^{2} - D - 2) y = 6 x + 6 e^{- x}