78.5.20 problem 4 (i)

Internal problem ID [18163]
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 (i)
Date solved : Tuesday, January 28, 2025 at 11:35:44 AM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 81

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

\begin{align*} y &= \frac {x \ln \left (x \right )+c_1 x -\sqrt {x \left (\ln \left (x \right )^{2} x +2 \ln \left (x \right ) c_1 x +c_1^{2} x +4\right )}}{2 x} \\ y &= \frac {x \ln \left (x \right )+c_1 x +\sqrt {x \left (\ln \left (x \right )^{2} x +2 \ln \left (x \right ) c_1 x +c_1^{2} x +4\right )}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.246 (sec). Leaf size: 77

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

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