2y^{''}-3y^'-2y=14t^2-4t-11

Lösung

2 y^{^{''}} - 3 y^{^{'}} - 2 y = 14 t^{2} - 4 t - 11

y = c_{1} e^{2 t} + c_{2} e^{- \frac{t}{2}} - 7 t^{2} + 23 t - 43

Schritte zur Lösung

2 y^{''} (t) - 3 y^{'} (t) - 2 y = 14 t^{2} - 4 t - 11

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- \frac{t}{2}} - 7 t^{2} + 23 t - 43

y = c_{1} e^{2 t} + c_{2} e^{- \frac{t}{2}} - 7 t^{2} + 23 t - 43

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

4 y^{^{''}} + y = 4 cos (x)

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

y^{^{''}} - 4 y^{^{'}} = 4 x

y^{^{''}} - 5 y^{^{'}} + 7 y = x e^{x}