Internal problem ID [10277]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 53. Change of
dependent variable. Page 125
Problem number: Ex 3.
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 }+2 y^{\prime } x -2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve((1+x^2)*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \left (\arctan \relax (x ) x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 23
DSolve[(1+x^2)*y''[x]+2*x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to i c_1 x-c_2 (x \text {ArcTan}(x)+1) \\ \end{align*}