Internal problem ID [7157]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 433.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 23
dsolve((1+x^2)*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (-3 x^{2}+1\right )+c_{2} \left (x^{3}-3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 33
DSolve[(1+x^2)*y''[x]-4*x*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3} i \left (c_2 \left (3 x^2-1\right )+3 c_1 (x-i)^3\right ) \\ \end{align*}