Internal problem ID [10869]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 2, First Order Equations. Problems page 149
Problem number: Problem 1(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } x +y-y^{2} x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x)+y(x)=x*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{\left (\ln \left (x \right )-c_{1} \right ) x} \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 22
DSolve[x*y'[x]+y[x]==x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-x \log (x)+c_1 x} \\ y(x)\to 0 \\ \end{align*}