49.16.3 problem 1(c)

Internal problem ID [7701]
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 : 1(c)
Date solved : Monday, January 27, 2025 at 03:10:05 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{4}+c_{2}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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