Internal problem ID [13672]
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 (f).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _exact, _linear, _homogeneous]]
\[ \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)-9*x*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} x^{6}+c_{4} x^{4}+x^{2} c_{3} +c_{1}}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[x^4*y''''[x]+6*x^3*y'''[x]-3*x^2*y''[x]-9*x*y'[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_4 x^3+\frac {c_1}{x^3}+c_3 x+\frac {c_2}{x} \]