78.8.44 problem 44

Internal problem ID [18242]
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 : 44
Date solved : Tuesday, January 28, 2025 at 11:43:29 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.137 (sec). Leaf size: 20

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

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