Internal problem ID [7806]
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]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-6 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve((x^2+1)*diff(y(x),x$2)-6*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x^{3}+x \right )+c_{2} \left (\frac {3 \arctan \left (x \right ) x^{3}}{2}+\frac {3 \arctan \left (x \right ) x}{2}+\frac {3 x^{2}}{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 36
DSolve[(x^2+1)*y''[x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \left (x^3+x\right )-\frac {1}{2} c_2 \left (3 \left (x^3+x\right ) \arctan (x)+3 x^2+2\right ) \]