78.8.34 problem 34

Internal problem ID [18232]
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. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 34
Date solved : Tuesday, January 28, 2025 at 11:42:56 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{2}+y+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.133 (sec). Leaf size: 21

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

\begin{align*} y(x)\to \frac {1}{x \log (x)+c_1 x} \\ y(x)\to 0 \\ \end{align*}