64.13.13 problem 13

Internal problem ID [13543]
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 : 13
Date solved : Tuesday, January 28, 2025 at 05:52:21 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(x^3*diff(y(x),x$3)-x^2*diff(y(x),x$2)-6*x*diff(y(x),x)+18*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{3} \ln \left (x \right ) x^{5}+c_{2} x^{5}+c_{1}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 26

DSolve[x^3*D[y[x],{x,3}]-x^2*D[y[x],{x,2}]-6*x*D[y[x],x]+18*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^5+c_3 x^5 \log (x)+c_1}{x^2} \]