Internal problem ID [5286]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 4. Linear equations with Regular Singular Points. Page 149
Problem number: 2(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 33
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*Pi*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = x^{-2 \sqrt {\pi }} c_{2}+x^{2 \sqrt {\pi }} c_{1}-\frac {x}{4 \pi -1} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 39
DSolve[x^2*y''[x]+x*y'[x]-4*Pi*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 x^{2 \sqrt {\pi }}+c_1 x^{-2 \sqrt {\pi }}+\frac {x}{1-4 \pi } \\ \end{align*}