Internal problem ID [7213]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 492.
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 }-10 x y^{\prime }+28 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 38
dsolve((1+x^2)*diff(y(x),x$2)-10*x*diff(y(x),x)+28*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (1+\frac {35}{3} x^{4}-14 x^{2}\right )+c_{2} \left (x^{7}+21 x^{5}-105 x^{3}+35 x \right ) \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 40
DSolve[(1+x^2)*y''[x]-10*x*y'[x]+28*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{105} c_2 \left (35 x^4-42 x^2+3\right )-c_1 (x-i)^6 (x+6 i) \\ \end{align*}