Internal problem ID [6970]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 239.
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 }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 35
dsolve(x^2*diff(y(x),x$2)-(2*sqrt(5)-1)*x*diff(y(x),x)+(19/4-3*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{-\frac {1}{2}+\sqrt {5}} \sinh \left (\sqrt {3}\, x \right )+c_{2} x^{-\frac {1}{2}+\sqrt {5}} \cosh \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 53
DSolve[x^2*y''[x]-(2*Sqrt[5]-1)*x*y'[x]+(19/4-3*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{-\sqrt {3} x} x^{\sqrt {5}-\frac {1}{2}} \left (\sqrt {3} c_2 e^{2 \sqrt {3} x}+6 c_1\right ) \\ \end{align*}