y^{''}+2y^'+5y=2sin(2t)

Lösung

y^{^{''}} + 2 y^{^{'}} + 5 y = 2 sin (2 t)

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{2}{17} sin (2 t) - \frac{8}{17} cos (2 t)

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 5 y = 2 sin (2 t)

Solve linear ODE:

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{2}{17} sin (2 t) - \frac{8}{17} cos (2 t)

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{2}{17} sin (2 t) - \frac{8}{17} cos (2 t)

\int tan^{2} (3 x) sec^{4} (3 x) d x

\int (csc^{2} (x) - 1) cot (x) d x

\frac{d}{d x} (\frac{1}{6 x - 7})

x \to - 1 lim (3 x^{2} - 3 x + 3)

\frac{d}{d x} ((- 1)^{n} x^{n})