59.1.820 problem 844

Internal problem ID [9992]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 844
Date solved : Monday, January 27, 2025 at 06:16:31 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} y^{\prime \prime }&=\frac {2 y}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)=((4*(3/2)^2-1)/(4*x^2))*y(x),y(x), singsol=all)
 

\[ y = \frac {c_{2} x^{3}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 18

DSolve[D[y[x],{x,2}]==((4*(3/2)^2-1)/(4*x^2))*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^3+c_1}{x} \]