y^{''''}-16y=xe^{2x}

Lösung

y^{^{''''}} - 16 y = x e^{2 x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} cos (2 x) + c_{4} sin (2 x) + \frac{e ^{2 x} x ^{2}}{64} - \frac{3 e ^{2 x} x}{128}

Schritte zur Lösung

y^{(4)} (x) - 16 y = x e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} cos (2 x) + c_{4} sin (2 x) + \frac{e ^{2 x} x ^{2}}{64} - \frac{3 e ^{2 x} x}{128}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} cos (2 x) + c_{4} sin (2 x) + \frac{e ^{2 x} x ^{2}}{64} - \frac{3 e ^{2 x} x}{128}

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

y^{^{''}} + y = cos (4 x)

y^{^{''}} - 8 y^{^{'}} + 16 y = \frac{e ^{- 4 x}}{1 + x ^{2}}

y^{^{''''}} - 4 y^{^{''}} = t^{2} - e^{t}

y^{^{''}} - 2 y^{^{'}} + y = \frac{9 e ^{t}}{1 + t ^{2}}