Internal problem ID [13350]
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 (d).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 y^{\prime } x -8 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)+7*x*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
\[ y = c_{1} x^{2}+\ln \left (x \right ) x^{2} c_{2} +\ln \left (x \right )^{2} x^{2} c_{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[x^3*y'''[x]-3*x^2*y''[x]+7*x*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 \left (c_3 \log ^2(x)+c_2 \log (x)+c_1\right ) \]