q^{''}+0.1q^'+q=vsin(0.5t),q(0)=0

Lösung

q^{^{''}} + 0.1 q^{^{'}} + q = v sin (0.5 t), q (0) = 0

q (t) = e^{- \frac{t}{20}} (0.08849 \dots v cos (\frac{399 t}{20}) + c_{2} sin (\frac{399 t}{20})) + 1.32743 \dots v sin (0.5 t) - 0.08849 \dots v cos (0.5 t)

Schritte zur Lösung

q^{''} (t) + 0.1 q^{'} (t) + q (t) = v sin (0.5 t)

Solve linear ODE:

q (t) = e^{- \frac{t}{20}} (0.08849 \dots v cos (\frac{399 t}{20}) + c_{2} sin (\frac{399 t}{20})) + 1.32743 \dots v sin (0.5 t) - 0.08849 \dots v cos (0.5 t)

q (t) = e^{- \frac{t}{20}} (0.08849 \dots v cos (\frac{399 t}{20}) + c_{2} sin (\frac{399 t}{20})) + 1.32743 \dots v sin (0.5 t) - 0.08849 \dots v cos (0.5 t)

y^{^{''}} - 2 y^{^{'}} = x + e^{x}

y^{^{''}} + 4 y^{^{'}} + 3 y = 30 e^{2 t}

y^{^{''}} + 25 y = 14 cos (5 x) + 21 sin (5 x)

l in e a r y^{^{''}} - y = t, y (0) = 0, y^{^{'}} (0) = 1

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