73.7.14 problem 14

Internal problem ID [15172]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 07:39:59 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 31

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

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