49.16.1 problem 1(a)

Internal problem ID [7699]
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(a)
Date solved : Monday, January 27, 2025 at 03:10:02 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{5}+c_{2}}{x^{3}} \]

✓ Solution by Mathematica

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

DSolve[x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^5+c_1}{x^3} \]