2y^{''}+11y^'+8y=0,y(0)=5,y^'(0)=0

Lösung

2 y^{^{''}} + 11 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y = (5 + \frac{- 5 57 + 55}{2 57}) e^{\frac{( - 11 + 57 ) t}{4}} - \frac{- 5 57 + 55}{2 57} e^{\frac{( - 11 - 57 ) t}{4}}

Schritte zur Lösung

2 y^{''} (t) + 11 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = (5 + \frac{- 5 57 + 55}{2 57}) e^{\frac{( - 11 + 57 ) t}{4}} - \frac{- 5 57 + 55}{2 57} e^{\frac{( - 11 - 57 ) t}{4}}

y = (5 + \frac{- 5 57 + 55}{2 57}) e^{\frac{( - 11 + 57 ) t}{4}} - \frac{- 5 57 + 55}{2 57} e^{\frac{( - 11 - 57 ) t}{4}}

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 3, y^{^{'}} (0) = 16

\frac{3}{4} x^{^{''}} + 192 x = 0, x (0) = - \frac{1}{4}, x^{^{'}} (0) = 0

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

\frac{1}{2} x^{^{''}} + 25 x = 0

3 y^{^{''}} - 24 y^{^{'}} = - 48 y