Internal problem ID [8327]
Book: Collection of Kovacic problems
Section: section 3. Problems from Kovacic related papers
Problem number: Kovacic 1985 paper. page 14. section 3.2, example 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\left (-1+\frac {6}{x^{2}}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve(diff(y(x),x$2)= ( (4*(5/2)^2-1)/(4*x^2)-1)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (\cos \left (x \right ) x^{2}-3 x \sin \left (x \right )-3 \cos \left (x \right )\right )}{x^{2}}+\frac {c_{2} \left (x^{2} \sin \left (x \right )+3 \cos \left (x \right ) x -3 \sin \left (x \right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 21
DSolve[y''[x]== ( (4*(5/2)^2-1)/(4*x^2)-1)*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (c_1 j_2(x)-c_2 y_2(x)) \]