Internal problem ID [8153]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 678.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
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)
\[ y \left (x \right ) = \frac {c_{1} x^{\sqrt {5}} \sinh \left (\sqrt {3}\, x \right )}{\sqrt {x}}+\frac {c_{2} x^{\sqrt {5}} \cosh \left (\sqrt {3}\, x \right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.086 (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]
\[ y(x)\to \frac {1}{6} e^{-\sqrt {3} x} x^{\sqrt {5}-\frac {1}{2}} \left (\sqrt {3} c_2 e^{2 \sqrt {3} x}+6 c_1\right ) \]