49.14.2 problem 2

Internal problem ID [7685]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 3. Linear equations with variable coefficients. Page 124
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:09:48 PM
CAS classification : [[_Emden, _Fowler]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

\[ y = x \left (c_{2} \ln \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 15

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

\[ y(x)\to x (c_2 \log (x)+c_1) \]