Chapter 4.6, Problem 27E

In Problems 27 and 28 the indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, ∞). Find the general solution of the given nonhomogeneous equation.

27. $x^{2}y″+xy\prime +\left(x^2-\frac{1}{4}\right)y=x^{3/2}$;

y₁= x^−1/2 cos x, y₂ = x^−1/2 sin x