y^{''}+y^'-6y=-22t+12t^2

Lösung

y^{^{''}} + y^{^{'}} - 6 y = - 22 t + 12 t^{2}

y = c_{1} e^{2 t} + c_{2} e^{- 3 t} - 2 t^{2} + 3 t - \frac{1}{6}

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 6 y = - 22 t + 12 t^{2}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 3 t} - 2 t^{2} + 3 t - \frac{1}{6}

y = c_{1} e^{2 t} + c_{2} e^{- 3 t} - 2 t^{2} + 3 t - \frac{1}{6}

y^{^{''}} + 4 y = - t^{2}

x^{^{''}} - 9 x = - 13 cos (2 t)

y^{^{''}} + y = x cos (2 x)

y^{^{''}} - 4 y = sinh (2 x)

y^{^{''}} + 6 y^{^{'}} + 5 y = 36 e^{x}, y (0) = - 2