y^{'''}+3.1y^{''}+3.1y^'+y=0

Lösung

y^{^{'''}} + 3.1 y^{^{''}} + 3.1 y^{^{'}} + y = 0

y = c_{1} e^{- t} + c_{2} e^{\frac{( - 21 + 41 ) t}{20}} + c_{3} e^{\frac{( - 21 - 41 ) t}{20}}

Schritte zur Lösung

y^{'''} (t) + 3.1 y^{''} (t) + 3.1 y^{'} (t) + y = 0

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{\frac{( - 21 + 41 ) t}{20}} + c_{3} e^{\frac{( - 21 - 41 ) t}{20}}

y = c_{1} e^{- t} + c_{2} e^{\frac{( - 21 + 41 ) t}{20}} + c_{3} e^{\frac{( - 21 - 41 ) t}{20}}

y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = \frac{2}{5}, y^{^{'}} (0) = \frac{2}{5}

y^{^{''}} + 20 y^{^{'}} + 36 y = 0, y^{^{'}} (0) = 0, y (0) = 5

- 2 y^{^{''}} + 8 y^{^{'}} = 0, y (- 1) = 2, y^{^{'}} (2) = 2

y^{^{''}} + 7 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = 9

y^{^{''}} = - y^{^{'}} - y