y^{''}+3y^'+2y=18+e^x

Lösung

y^{^{''}} + 3 y^{^{'}} + 2 y = 18 + e^{x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 9 + \frac{1}{6} e^{x}

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) + 2 y = 18 + e^{x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 9 + \frac{1}{6} e^{x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 9 + \frac{1}{6} e^{x}

y^{^{''}} + 49 y = cos (7 t)

y^{^{''}} - 9 y = 12 cos (3 x)

y^{^{''}} + 4 y = 60 x \cdot e^{2 x}

y^{^{''}} + 6 y^{^{'}} + \frac{1}{15} y = 450

y^{^{''}} - y = t - e^{- t}