9y^{''}+10y=0,y(pi)=1

解

9 y^{^{''}} + 10 y = 0, y (π) = 1

y = \frac{cos ( \frac{10 t}{3} ) ( 1 - sin ( \frac{10 π}{3} ) c _{2} )}{cos ( \frac{10 π}{3} )} + c_{2} sin (\frac{10 t}{3})

解答ステップ

9 y^{''} (t) + 10 y = 0

線形 ODE を解く:

y = \frac{cos ( \frac{10 t}{3} ) ( 1 - sin ( \frac{10 π}{3} ) c _{2} )}{cos ( \frac{10 π}{3} )} + c_{2} sin (\frac{10 t}{3})

y = \frac{cos ( \frac{10 t}{3} ) ( 1 - sin ( \frac{10 π}{3} ) c _{2} )}{cos ( \frac{10 π}{3} )} + c_{2} sin (\frac{10 t}{3})