y^{''}+y^'+12y=0,y(0)=1

Lösung

y^{^{''}} + y^{^{'}} + 12 y = 0, y (0) = 1

y = e^{- \frac{t}{2}} (cos (\frac{47 t}{2}) + c_{2} sin (\frac{47 t}{2}))

Schritte zur Lösung

y^{''} (t) + y^{'} (t) + 12 y = 0

Solve linear ODE:

y = e^{- \frac{t}{2}} (cos (\frac{47 t}{2}) + c_{2} sin (\frac{47 t}{2}))

y = e^{- \frac{t}{2}} (cos (\frac{47 t}{2}) + c_{2} sin (\frac{47 t}{2}))

2 y^{^{''}} - y = 0

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 6 y^{^{'}} + 5 y = 0, y (0) = 3, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} = 0, y^{^{'}} (0) = 3, y (0) = 0

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = a, y^{^{'}} (0) = 2