59.1.744 problem 764

Internal problem ID [9916]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 764
Date solved : Monday, January 27, 2025 at 06:15:44 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

dsolve((x^2+1)*diff(y(x),x$2)-6*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {3 x c_{2} \left (x^{2}+1\right ) \arctan \left (x \right )}{2}+c_{1} x^{3}+\frac {3 c_{2} x^{2}}{2}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 33

DSolve[(x^2+1)*D[y[x],{x,2}]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^3+x\right ) \left (c_2 \int _1^x\frac {1}{\left (K[1]^3+K[1]\right )^2}dK[1]+c_1\right ) \]