y^{''}+18y^'+81y=x

Lösung

y^{^{''}} + 18 y^{^{'}} + 81 y = x

y = c_{1} e^{- 9 x} + c_{2} x e^{- 9 x} + \frac{x}{81} - \frac{2}{729}

Schritte zur Lösung

y^{''} (x) + 18 y^{'} (x) + 81 y = x

Solve linear ODE:

y = c_{1} e^{- 9 x} + c_{2} x e^{- 9 x} + \frac{x}{81} - \frac{2}{729}

y = c_{1} e^{- 9 x} + c_{2} x e^{- 9 x} + \frac{x}{81} - \frac{2}{729}