y^{'''}+2y^{''}-y^'-2y=5-4x^3

Lösung

y^{^{'''}} + 2 y^{^{''}} - y^{^{'}} - 2 y = 5 - 4 x^{3}

y = c_{1} e^{- 2 x} + c_{2} e^{- x} + c_{3} e^{x} + 2 x^{3} - 3 x^{2} + 15 x - 10

Schritte zur Lösung

y^{'''} (x) + 2 y^{''} (x) - y^{'} (x) - 2 y = 5 - 4 x^{3}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- x} + c_{3} e^{x} + 2 x^{3} - 3 x^{2} + 15 x - 10

y = c_{1} e^{- 2 x} + c_{2} e^{- x} + c_{3} e^{x} + 2 x^{3} - 3 x^{2} + 15 x - 10

y^{^{''}} - y = 7 t

y^{^{''}} - 4 y = cos (3 x)

y^{^{''}} + 3 y^{^{'}} + 21 y = 9 cos (4 t)

4 y^{^{''}} + 7 y^{^{'}} - y = 15

y^{^{''}} + 7 y^{^{'}} + 12 y = 5 e^{- 6 x}