Internal problem ID [13349]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 20. Euler equations. Additional exercises page 382
Problem number: 20.4 (c).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(x^3*diff(y(x),x$3)-5*x^2*diff(y(x),x$2)+14*x*diff(y(x),x)-18*y(x)=0,y(x), singsol=all)
\[ y = c_{1} x^{2}+c_{2} x^{3}+c_{3} x^{3} \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 22
DSolve[x^3*y'''[x]-5*x^2*y''[x]+14*x*y'[x]-18*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 (c_2 x+c_3 x \log (x)+c_1) \]