2y^{''}+5y^'+2y=x^3+9e^{4x}

Lösung

2 y^{^{''}} + 5 y^{^{'}} + 2 y = x^{3} + 9 e^{4 x}

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- 2 x} + \frac{x ^{3}}{2} + \frac{- 15 x ^{2} + 63 x}{4} - \frac{255}{8} + \frac{1}{6} e^{4 x}

Schritte zur Lösung

2 y^{''} (x) + 5 y^{'} (x) + 2 y = x^{3} + 9 e^{4 x}

Solve linear ODE:

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- 2 x} + \frac{x ^{3}}{2} + \frac{- 15 x ^{2} + 63 x}{4} - \frac{255}{8} + \frac{1}{6} e^{4 x}

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- 2 x} + \frac{x ^{3}}{2} + \frac{- 15 x ^{2} + 63 x}{4} - \frac{255}{8} + \frac{1}{6} e^{4 x}

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

y^{^{''}} - 4 y^{^{'}} + 3 y = 2 t

3 x^{^{''}} + 108 x = 15 e^{- 5 t} cos (4 t)

y^{^{''}} + y^{^{'}} - 27 = x e^{x}

y^{^{''}} + 5 y^{^{'}} - 9 y = e^{4 x}