2y^{''}+y^'+3y=3cos(3t)+2sin(3t)

Lösung

2 y^{^{''}} + y^{^{'}} + 3 y = 3 cos (3 t) + 2 sin (3 t)

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{23 t}{4}) + c_{2} sin (\frac{23 t}{4})) - \frac{7}{78} sin (3 t) - \frac{17}{78} cos (3 t)

Schritte zur Lösung

2 y^{''} (t) + y^{'} (t) + 3 y = 3 cos (3 t) + 2 sin (3 t)

Solve linear ODE:

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{23 t}{4}) + c_{2} sin (\frac{23 t}{4})) - \frac{7}{78} sin (3 t) - \frac{17}{78} cos (3 t)

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{23 t}{4}) + c_{2} sin (\frac{23 t}{4})) - \frac{7}{78} sin (3 t) - \frac{17}{78} cos (3 t)

\int_{0}^{2} π (2 x - x^{2})^{2} d x

\frac{d}{d x} (e^{x} cos (6 x))

\int_{- 1}^{3} (x^{3} + 5 x) d x

y \to \infty lim (e^{y})

\int 2 x x^{2} + 2 d x