49.16.2 problem 1(b)

Internal problem ID [7700]
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(b)
Date solved : Monday, January 27, 2025 at 03:10:03 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

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

\[ y(x)\to \frac {c_1}{\sqrt {x}}+c_2 x \]