Internal problem ID [7563]
Book: Collection of Kovacic problems
Section: section 2. Solution found using all possible Kovacic cases
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {12 y}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)=((4*(7/2)^2-1)/(4*x^2))*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x^{3}}+c_{2} x^{4} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[y''[x]==((4*(7/2)^2-1)/(4*x^2))*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^7+c_1}{x^3} \\ \end{align*}