(D^3+8)y=x^4+2x+1

Lösung

(D^{3} + 8) y = x^{4} + 2 x + 1

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

Schritte zur Lösung

(D^{3} + 8) y = x^{4} + 2 x + 1

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 13 y = 13

y^{^{''}} + 4 y = 16 t

y^{^{''}} - 8 y^{^{'}} + 16 y = e^{4 t} ln (t)

10 y^{^{''}} + 1000 y = 100 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y^{^{'}} + 14 y = 2 + t, y (0) = 1, y^{^{'}} (0) = 1