Internal problem ID [13673]
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 (g).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x^4*diff(y(x),x$4)+2*x^3*diff(y(x),x$3)+x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x \left (c_{1} +c_{2} \ln \left (x \right )+c_{3} \ln \left (x \right )^{2}+c_{4} \ln \left (x \right )^{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 29
DSolve[x^4*y''''[x]+2*x^3*y'''[x]+x^2*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (c_4 \log ^3(x)+c_3 \log ^2(x)+c_2 \log (x)+c_1\right ) \]