q^{''}+2q^'+1/(0.25)q=50cos(sqrt(3)t)

Lösung

q^{^{''}} + 2 q^{^{'}} + \frac{1}{0.25} q = 50 cos (3 t)

q (t) = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{100 3}{13} sin (3 t) + \frac{50}{13} cos (3 t)

Schritte zur Lösung

q^{''} (t) + 2 q^{'} (t) + \frac{1}{0.25} q (t) = 50 cos (3 t)

Solve linear ODE:

q (t) = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{100 3}{13} sin (3 t) + \frac{50}{13} cos (3 t)

q (t) = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{100 3}{13} sin (3 t) + \frac{50}{13} cos (3 t)

\frac{\partial}{\partial y} (x arctan (x + 2 y))

d er i v a t i v e e^{x} - e^{- x} - 2 x

\int 2 x (x^{2} + 1)^{- 6} d x

d er i v a t i v e f (t) = \frac{1}{( t ^{2} + 3 t + 1 ) ^{\frac{5}{2}}}

\int 1 - e^{x} d x