15.18.8 problem 8

Internal problem ID [3251]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 8
Date solved : Monday, January 27, 2025 at 07:28:46 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y \left (x \right ) = -x +\left (c_{1} +1\right ) \arctan \left (x \right )+c_2 \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 18

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

\[ y(x)\to (1+c_1) \arctan (x)-x+c_2 \]