8.1.2.46 Second order differential equations

Problem: Find the value of the particular solution of the differential equation at the point \( x_{0} \), satisfying given initial conditions: \[ y^{\prime \prime}=2 \sin x \cdot \cos ^{2} x, y(0)=-\frac{5}{9}, \quad y^{\prime}(0)=-\frac{2}{3}, \quad x_{0}=\frac{\pi}{2} . \] clip2net.com