31.1.23 problem 10.5

Internal problem ID [5721]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 10.5
Date solved : Monday, January 27, 2025 at 01:11:33 PM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.167 (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*}