Internal problem ID [8315]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 844.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {y^{\prime \prime }-\frac {2 y}{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)=((4*(3/2)^2-1)/(4*x^2))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x}+c_{2} x^{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 18
DSolve[y''[x]==((4*(3/2)^2-1)/(4*x^2))*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 x^3+c_1}{x} \]