y^{''}+y= 1/((cos(2x))^{3/2)}

解

y^{^{''}} + y = \frac{1}{( cos ( 2 x ) ) ^{\frac{3}{2}}}

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) \cdot \int - sin (x) sec^{\frac{3}{2}} (2 x) d x + sin (x) \cdot \int cos (x) sec^{\frac{3}{2}} (2 x) d x

解答ステップ

y^{''} (x) + y = \frac{1}{( cos ( 2 x ) ) ^{\frac{3}{2}}}

線形 ODE を解く:

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) \cdot \int - sin (x) sec^{\frac{3}{2}} (2 x) d x + sin (x) \cdot \int cos (x) sec^{\frac{3}{2}} (2 x) d x

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) \cdot \int - sin (x) sec^{\frac{3}{2}} (2 x) d x + sin (x) \cdot \int cos (x) sec^{\frac{3}{2}} (2 x) d x