y^{''}-9y=-27t+18t^2

Lösung

y^{^{''}} - 9 y = - 27 t + 18 t^{2}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - 2 t^{2} + 3 t - \frac{4}{9}

Schritte zur Lösung

y^{''} (t) - 9 y = - 27 t + 18 t^{2}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - 2 t^{2} + 3 t - \frac{4}{9}

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - 2 t^{2} + 3 t - \frac{4}{9}

y^{^{'''}} - 2 y^{^{''}} + 26 y^{^{'}} = 174 e^{3 x}

y^{^{''}} + y^{^{'}} - y = t^{3}, y (0) = 1, y^{^{'}} (0) = 0

- y^{^{''}} + 2 y^{^{'}} + 3 y = 1, y (0) = 0, y (1) = (0)

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

y^{^{''}} + (9 - 2) y^{^{'}} - 2 (9) y = 8 e^{2 x}