4y^{''}-y=0,y(-9)=1,y^'(-9)=-1

解

4 y^{^{''}} - y = 0, y (- 9) = 1, y^{^{'}} (- 9) = - 1

y = (e^{\frac{9}{2}} - \frac{3 e ^{\frac{9}{2}}}{2}) e^{\frac{t}{2}} + \frac{3 e ^{\frac{- t - 9}{2}}}{2}

解答ステップ

4 y^{''} (t) - y = 0

線形 ODE を解く:

y = (e^{\frac{9}{2}} - \frac{3 e ^{\frac{9}{2}}}{2}) e^{\frac{t}{2}} + \frac{3 e ^{\frac{- t - 9}{2}}}{2}

y = (e^{\frac{9}{2}} - \frac{3 e ^{\frac{9}{2}}}{2}) e^{\frac{t}{2}} + \frac{3 e ^{\frac{- t - 9}{2}}}{2}