Internal problem ID [4157]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 8. Special second order equations. Lesson 35. Independent variable x
absent
Problem number: Exercise 35.15, page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 15
dsolve((1+x^2)*diff(y(x),x$2)+2*x*(diff(y(x),x)+1)=0,y(x), singsol=all)
\[ y \relax (x ) = -x +\arctan \relax (x ) c_{1}+\arctan \relax (x )+c_{2} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 18
DSolve[(1+x^2)*y''[x]+2*x*(y'[x]+1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (1+c_1) \text {ArcTan}(x)-x+c_2 \\ \end{align*}