73.8.6 problem 13.1 (f)

Internal problem ID [15214]
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)
Date solved : Tuesday, January 28, 2025 at 07:50:08 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 10

dsolve((x^2+1)*diff(y(x),x$2)+2*x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +\arctan \left (x \right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 26

DSolve[(x^2+1)*D[y[x],{x,2}]+2*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\frac {c_1}{K[1]^2+1}dK[1]+c_2 \]