y^{''}+8y^'+41y=0,y(0)=3,y^'(0)=-11

Lösung

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y (0) = 3, y^{^{'}} (0) = - 11

y = e^{- 4 t} (3 cos (5 t) + \frac{1}{5} sin (5 t))

Schritte zur Lösung

y^{''} (t) + 8 y^{'} (t) + 41 y = 0

Solve linear ODE:

y = e^{- 4 t} (3 cos (5 t) + \frac{1}{5} sin (5 t))

y = e^{- 4 t} (3 cos (5 t) + \frac{1}{5} sin (5 t))

y^{^{''}} - 6 y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = - 1, y^{^{'}} (0) = 0

2 x^{^{''}} + 2 x^{^{'}} + 7 x = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 20, y^{^{'}} (0) = 0

x^{^{''}} + 6 x^{^{'}} + 13 x = 0