Internal problem ID [11867]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 y^{\prime } x +18 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{3} x^{5} \ln \left (x \right )+c_{2} x^{5}+c_{1}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 26
DSolve[x^3*y'''[x]-x^2*y''[x]-6*x*y'[x]+18*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 x^5+c_3 x^5 \log (x)+c_1}{x^2} \]