y^{''''}-5y^{''}+4y=e^x(-122-48x+72x^2)

Lösung

y^{^{''''}} - 5 y^{^{''}} + 4 y = e^{x} (- 122 - 48 x + 72 x^{2})

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} e^{x} + c_{4} e^{- x} + \frac{e ^{x} ( - 8 x ^{3} + 4 x ^{2} + 10 x - 1 )}{2}

Schritte zur Lösung

y^{(4)} (x) - 5 y^{''} (x) + 4 y = e^{x} (- 122 - 48 x + 72 x^{2})

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} e^{x} + c_{4} e^{- x} + \frac{e ^{x} ( - 8 x ^{3} + 4 x ^{2} + 10 x - 1 )}{2}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} e^{x} + c_{4} e^{- x} + \frac{e ^{x} ( - 8 x ^{3} + 4 x ^{2} + 10 x - 1 )}{2}

y^{^{'''}} + 100 y^{^{'}} = tan (10 x)

1 x^{^{''}} - 3 x^{^{'}} + 2 x = 20 sin (2 t)

y^{^{'''}} + 2 y^{^{'}} = cos (x)

y^{^{'''}} = 3 y^{^{''}} + 9 (e^{2 x}) + 5 cos (x)

(D^{4} - 1) y = e^{- x}