Internal problem ID [7134]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 410.
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 }+\left (x^{2}-\frac {1}{4}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.152 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2-1/4)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \relax (x )}{\sqrt {x}}+\frac {c_{2} \cos \relax (x )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 19
DSolve[(1-x^2)*y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+c_2 \left (x \tanh ^{-1}(x)-1\right ) \\ \end{align*}