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

Lösung

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

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- x} + \frac{1}{10} e^{- 3 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- x} + \frac{1}{10} e^{- 3 x}

y = c_{1} e^{- \frac{x}{2}} + c_{2} e^{- x} + \frac{1}{10} e^{- 3 x}

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

y^{^{''}} - 4 y^{^{'}} + 4 y = (x + 1) e^{x}

y^{^{''}} - y^{^{'}} = e^{2} x, y (0) = 0, y (1) = 0

y^{^{''}} - 4 y = sin (x)

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