64.9.1 problem 1

Internal problem ID [13399]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 124
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 05:41:46 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 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: 0.002 (sec). Leaf size: 13

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

\[ y = x \left (c_{2} x^{3}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 16

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

\[ y(x)\to x \left (c_2 x^3+c_1\right ) \]