y^{''}+4y^'+4y=2x+3

Lösung

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 x + 3

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{x}{2} + \frac{1}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{x}{2} + \frac{1}{4}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{x}{2} + \frac{1}{4}

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 x + 4

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- t}

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

x^{^{''}} + 4 x = 4 t

y^{^{''}} + 16 y = g (t), y (0) = 3, y^{^{'}} (0) = 0