Internal problem ID [13667]
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 (a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} x^{4}+c_{1} x^{3}+c_{3}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 22
DSolve[x^3*y'''[x]+2*x^2*y''[x]-4*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 x^2+\frac {c_1}{x^2}+c_2 x \]