Internal problem ID [7440]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 721.
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: 0.172 (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)
\[ y \relax (x ) = \frac {c_{1} \sinh \relax (x )}{\sqrt {x}}+\frac {c_{2} \cosh \relax (x )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 32
DSolve[x^2*y''[x]+x*y'[x]-(x^2+1/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x} \left (c_2 e^{2 x}+2 c_1\right )}{2 \sqrt {x}} \\ \end{align*}