73.13.27 problem 20.4 (c)

Internal problem ID [15405]
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)
Date solved : Tuesday, January 28, 2025 at 07:54:42 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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)
 

\[ y = x^{2} \left (c_{3} \ln \left (x \right ) x +c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 22

DSolve[x^3*D[y[x],{x,3}]-5*x^2*D[y[x],{x,2}]+14*x*D[y[x],x]-18*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (c_2 x+c_3 x \log (x)+c_1) \]