Internal problem ID [13478]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.1 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve((x^2+1)*diff(y(x),x$2)+2*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +\arctan \left (x \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 13
DSolve[(x^2+1)*y''[x]+2*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \arctan (x)+c_2 \]