(D^2-D)y=e^xsin(x)

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

(D^{3} + 2 D^{2} - 5 D - 6) y = e^{- 3 x}

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

y^{^{''}} + 16 y = 17 sec^{2} (4 t)

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

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