6y^{''}+y^'-2y=0,y(1)=2,y^'(1)= 1/6

解

6 y^{^{''}} + y^{^{'}} - 2 y = 0, y (1) = 2, y^{^{'}} (1) = \frac{1}{6}

y = e^{\frac{3 t - 7}{6}} (2 e^{\frac{2}{3}} - \frac{5 e ^{\frac{2}{3}}}{7}) + \frac{5 e ^{\frac{2}{3}}}{7} e^{- \frac{2 t}{3}}

解答ステップ

6 y^{''} (t) + y^{'} (t) - 2 y = 0

線形 ODE を解く:

y = e^{\frac{3 t - 7}{6}} (2 e^{\frac{2}{3}} - \frac{5 e ^{\frac{2}{3}}}{7}) + \frac{5 e ^{\frac{2}{3}}}{7} e^{- \frac{2 t}{3}}

y = e^{\frac{3 t - 7}{6}} (2 e^{\frac{2}{3}} - \frac{5 e ^{\frac{2}{3}}}{7}) + \frac{5 e ^{\frac{2}{3}}}{7} e^{- \frac{2 t}{3}}