64.13.9 problem 9

Internal problem ID [13539]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 05:52:16 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(9*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 24

DSolve[9*x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \sqrt [3]{x} (c_2 \log (x)+3 c_1) \]