y^{'''}-2y^{''}-5y^'+6y=2e^x(1-6x)

Lösung

y^{^{'''}} - 2 y^{^{''}} - 5 y^{^{'}} + 6 y = 2 e^{x} (1 - 6 x)

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

Schritte zur Lösung

y^{'''} (x) - 2 y^{''} (x) - 5 y^{'} (x) + 6 y = 2 e^{x} (1 - 6 x)

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} - 2 y = 3 e^{2 x} - 4 e^{3 x}

x^{^{''}} + 3 x^{^{'}} + 33 x = 11 cos (5 t)

y^{^{''}} + 10 y^{^{'}} + 16 y = 12 cos (2 x) + 4 sin (2 x)

y^{^{'''}} - y^{^{''}} - 12 y^{^{'}} = x - 2 x e^{- 3 x}

y^{^{''}} + y = u_{3} (t), y (0) = 0, y^{^{'}} (0) = 1