2y^{''}+8y^'+80y=60cos(8t)

Lösung

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 60 cos (8 t)

y = e^{- 2 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{3}{5} sin (8 t) - \frac{9}{20} cos (8 t)

Schritte zur Lösung

2 y^{''} (t) + 8 y^{'} (t) + 80 y = 60 cos (8 t)

Solve linear ODE:

y = e^{- 2 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{3}{5} sin (8 t) - \frac{9}{20} cos (8 t)

y = e^{- 2 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{3}{5} sin (8 t) - \frac{9}{20} cos (8 t)

\frac{\partial}{\partial x} (e^{x + y})

n = 0 \sum \infty (x)^{n}

\int \frac{1}{t ^{4} + 16} d t

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

x \to 3 lim (\frac{x + 2}{x + 3})