73.13.25 problem 20.4 (a)

Internal problem ID [15403]
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)
Date solved : Tuesday, January 28, 2025 at 07:54:41 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = \frac {c_{1} x^{4}+c_{3} x^{3}+c_{2}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 22

DSolve[x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 x^2+\frac {c_1}{x^2}+c_2 x \]