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

Lösung

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

y = c_{1} e^{(- 1 + 3) x} + c_{2} e^{(- 1 - 3) x} + \frac{- x ^{2} - 3}{2} - x - \frac{8}{73} e^{x} sin (2 x) + \frac{3}{73} e^{x} cos (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{(- 1 + 3) x} + c_{2} e^{(- 1 - 3) x} + \frac{- x ^{2} - 3}{2} - x - \frac{8}{73} e^{x} sin (2 x) + \frac{3}{73} e^{x} cos (2 x)

y = c_{1} e^{(- 1 + 3) x} + c_{2} e^{(- 1 - 3) x} + \frac{- x ^{2} - 3}{2} - x - \frac{8}{73} e^{x} sin (2 x) + \frac{3}{73} e^{x} cos (2 x)

(D^{4} + 2 D^{3} - 3 D^{2}) y = 3 e^{2 x} + 4 sin (x)

y^{^{'''}} - 4 y^{^{''}} + y^{^{'}} + 6 y = 3 e^{4 t}

y^{^{''}} + 4 y = sin (t) - H (t - 2 π) sin (t - 2 π)

y^{^{''}} + y = sin (a t)

y^{^{''}} - 4 y^{^{'}} + 13 y = 24 e^{2 x} cos (3 x)