(D^4-4D^2)y=5x^2-e^{2x}

Lösung

(D^{4} - 4 D^{2}) y = 5 x^{2} - e^{2 x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} + c_{4} x - \frac{5 x ^{4}}{48} + \frac{- 5 x ^{2} - e ^{2 x} x}{16}

Schritte zur Lösung

(D^{4} - 4 D^{2}) y = 5 x^{2} - e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} + c_{4} x - \frac{5 x ^{4}}{48} + \frac{- 5 x ^{2} - e ^{2 x} x}{16}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} + c_{4} x - \frac{5 x ^{4}}{48} + \frac{- 5 x ^{2} - e ^{2 x} x}{16}

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

y^{^{''}} + 25 y = 50 sin (5 t)

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

y^{^{''}} + 2 y^{^{'}} + y = t^{5} e^{- 5 t}

y^{^{''}} + 16 y = 9 (t) - 9 (t - 98 π), y (0) = 0, y^{^{'}} (0) = 0