Let’s consider the second order linear nonhomogeneous Euler differential equation \(x^2y\,^{\prime \prime }+5xy\,^{\prime }+4y=\dfrac {2}{x^2}\) on \((0,\infty )\).

(a)
Let’s determine the general solution to the complementary equation to this Euler differential equation.
(b)
Let’s use Reduction of Order to determine the general solution to this Euler equation on \((0,\infty )\).
(c)
Let’s solve the IVP \(x^2y\,^{\prime \prime }+5xy\,^{\prime }+4y=\dfrac {2}{x^2}\), \(y(1)=1\), \(y'(1)=1\) on \((0,\infty )\).