Internal problem ID [4003]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.18, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x y^{\prime }+y^{2} x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)+x*y(x)^2-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x}{x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 23
DSolve[x*y'[x]+x*y[x]^2-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x}{x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}