78.1.20 problem 2 (f)

Internal problem ID [18075]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (f)
Date solved : Tuesday, January 28, 2025 at 11:25:31 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 18

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

\[ y(x)\to \frac {1}{2} \log \left (x^2+1\right )+c_1 \]