x^{''}+x^'+3x=0,x(0)=1,x^'(0)=2

Lösung

x^{^{''}} + x^{^{'}} + 3 x = 0, x (0) = 1, x^{^{'}} (0) = 2

x = e^{- \frac{t}{2}} (cos (\frac{11 t}{2}) + \frac{5}{11} sin (\frac{11 t}{2}))

Schritte zur Lösung

x^{''} (t) + x^{'} (t) + 3 x = 0

Solve linear ODE:

x = e^{- \frac{t}{2}} (cos (\frac{11 t}{2}) + \frac{5}{11} sin (\frac{11 t}{2}))

x = e^{- \frac{t}{2}} (cos (\frac{11 t}{2}) + \frac{5}{11} sin (\frac{11 t}{2}))

y^{^{''''}} - 8 y^{^{'''}} = 0

y^{^{'''}} - 2 y^{^{''}} + 5 y^{^{'}} = 0

4 y^{^{''}} - 5 y^{^{'}} + y = 0, y (0) = 4, y^{^{'}} (0) = \frac{1}{4}

2 y^{^{''}} + 10 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = 0, y^{^{'}} (0) = 0