Internal problem ID [7518]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 801.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.155 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+1/4*(x^2-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (\frac {x}{2}\right )}{\sqrt {x}}+\frac {c_{2} \cos \left (\frac {x}{2}\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 35
DSolve[x^2*y''[x]+x*y'[x]+1/4*(x^2-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {i x}{2}} (c_2 (\sin (x)-i \cos (x))+c_1)}{\sqrt {x}} \\ \end{align*}