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

Lösung

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

y = e^{- \frac{t}{2}} (cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{t}{2}} (cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

y = e^{- \frac{t}{2}} (cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

y^{^{'''}} + y^{^{''}} - 22 y^{^{'}} - 40 y = 0

y^{^{''}} + 11 y^{^{'}} + 10 y = 0

81 y^{^{''}} - 144 y^{^{'}} + 73 y = 0, y (1) = 6, y^{^{'}} (1) = 5

y^{^{''}} + 9 y^{^{'}} + 8 y = 0, y (0) = 6, y^{^{'}} (0) = - 1

y^{^{''''}} + 4 y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} - 12 y = 0