2y^{''}+14y^'+8y=0,y(0)=5,y^'(0)=0

Lösung

2 y^{^{''}} + 14 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y = (5 + \frac{- 5 33 + 35}{2 33}) e^{\frac{( - 7 + 33 ) t}{2}} - \frac{- 5 33 + 35}{2 33} e^{- \frac{( 7 + 33 ) t}{2}}

Schritte zur Lösung

2 y^{''} (t) + 14 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = (5 + \frac{- 5 33 + 35}{2 33}) e^{\frac{( - 7 + 33 ) t}{2}} - \frac{- 5 33 + 35}{2 33} e^{- \frac{( 7 + 33 ) t}{2}}

y = (5 + \frac{- 5 33 + 35}{2 33}) e^{\frac{( - 7 + 33 ) t}{2}} - \frac{- 5 33 + 35}{2 33} e^{- \frac{( 7 + 33 ) t}{2}}

4 y^{^{''}} + 7 y^{^{'}} + 3 y = 0

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (- 1) = 5, y^{^{'}} (- 1) = 2

c y^{^{''}} + ab y^{^{'}} = 0, y (0) = 1, y (1.2) = 0

y^{^{''}} + 4 y^{^{'}} = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + 65 y = 0, y (0) = - 1, y^{^{'}} (0) = 33