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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - 5 y^{^{'}} = 8 e^{4} t - 4 e - t, y (0) = 1, y^{^{'}} (0) = - 1

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

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{2 x} + 4 x e^{x}

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

y^{^{'''}} - 2 y^{^{''}} + 4 y^{^{'}} - 8 y = 8 sin (2 x)