49.16.5 problem 1(e)

Internal problem ID [7703]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 4. Linear equations with Regular Singular Points. Page 149
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:10:08 PM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_3 \,x^{2} \ln \left (x \right )+c_{2} x^{2}+c_{1}}{x} \]

✓ 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}]-x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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