59.1.389 problem 400

Internal problem ID [9561]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 400
Date solved : Monday, January 27, 2025 at 06:04:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

dsolve(x^3*diff(y(x),x$2)+ diff(y(x),x)-1/x*y(x) = 0,y(x), singsol=all)
 

\[ y = x \left (c_{1} +c_{2} \operatorname {erf}\left (\frac {i \sqrt {2}}{2 x}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 34

DSolve[x^3*D[y[x],{x,2}]+ D[y[x],x]-1/x*y[x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x-\sqrt {\frac {\pi }{2}} c_2 x \text {erfi}\left (\frac {1}{\sqrt {2} x}\right ) \]