Internal problem ID [7124]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 400.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x^3*diff(y(x),x$2)+ diff(y(x),x)-1/x*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = x c_{1} +c_{2} x \,\operatorname {erf}\left (\frac {i \sqrt {2}}{2 x}\right ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 34
DSolve[x^3*y''[x]+ y'[x]-1/x*y[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\sqrt {\frac {\pi }{2}} c_2 x \text {erfi}\left (\frac {1}{\sqrt {2} x}\right ) \\ \end{align*}