Internal problem ID [7050]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 320.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve((x^2+1)*diff(y(x),x$2)-6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{3}+x \right )+c_{2} \left (\frac {\left (3 x^{3}+3 x \right ) \arctan \relax (x )}{2}+\frac {3 x^{2}}{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 36
DSolve[(x^2+1)*y''[x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x^3+x\right )-\frac {1}{2} c_2 \left (3 \left (x^3+x\right ) \text {ArcTan}(x)+3 x^2+2\right ) \\ \end{align*}