5y^{''}+6y^'+5/(1.96)y=3cos(2t)

Lösung

5 y^{^{''}} + 6 y^{^{'}} + \frac{5}{1.96} y = 3 cos (2 t)

y = e^{- 0.6 t} (c_{1} cos (0.38756 \dots t) + c_{2} sin (0.38756 \dots t)) + 0.08027 \dots sin (2 t) - 0.11672 \dots cos (2 t)

Schritte zur Lösung

5 y^{''} (t) + 6 y^{'} (t) + \frac{5}{1.96} y = 3 cos (2 t)

Solve linear ODE:

y = e^{- 0.6 t} (c_{1} cos (0.38756 \dots t) + c_{2} sin (0.38756 \dots t)) + 0.08027 \dots sin (2 t) - 0.11672 \dots cos (2 t)

y = e^{- 0.6 t} (c_{1} cos (0.38756 \dots t) + c_{2} sin (0.38756 \dots t)) + 0.08027 \dots sin (2 t) - 0.11672 \dots cos (2 t)

y^{^{''}} + 200 y^{^{'}} + 1000000 = 0

f^{^{''}} (t) + f (t) = cos (t)

y^{^{''}} + 3 y^{^{'}} + 2 y = 3 e^{- 4 t}, y (0) = 1

y^{^{''}} - y^{^{'}} = e^{- 3 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 8 y^{^{'}} + 16 = 0, y (0) = 1, y^{^{'}} (0) = 0