49.16.9 problem 2(d)

Internal problem ID [7707]
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)
Date solved : Monday, January 27, 2025 at 03:10:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y&=x \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 44

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*Pi*y(x)=x,y(x), singsol=all)
 

\[ y = \frac {c_{2} \left (4 \pi -1\right ) x^{-2 \sqrt {\pi }}+c_{1} \left (4 \pi -1\right ) x^{2 \sqrt {\pi }}-x}{4 \pi -1} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 39

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-4*Pi*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^{2 \sqrt {\pi }}+c_1 x^{-2 \sqrt {\pi }}+\frac {x}{1-4 \pi } \]