78.5.12 problem 4 (a)

Internal problem ID [18155]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 4 (a)
Date solved : Tuesday, January 28, 2025 at 11:34:22 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

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

\begin{align*} y &= \frac {c_1}{2}-\frac {\sqrt {c_1^{2}-4 x +4}}{2} \\ y &= \frac {c_1}{2}+\frac {\sqrt {c_1^{2}-4 x +4}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.256 (sec). Leaf size: 56

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

\begin{align*} y(x)\to \frac {1}{2} \left (c_1-\sqrt {-4 x+4+c_1{}^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {-4 x+4+c_1{}^2}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}