Chapter 3.6, Problem 15P

To determine

To verify: Whether the functions $y_1\left(x\right)=x^{-\frac{1}{2}}\sin x$ and $y_2\left(x\right)=x^{-\frac{1}{2}}\cos x$ satisfies the corresponding homogeneous equation of the differential equation $x^2{y}^{″}+x{y}^{\prime }+\left(x^2-0.25\right)y=g\left(x\right),x>0$ and compute the particular solution.