Internal problem ID [4005]
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 11.20, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 18
dsolve(x^2*(x-1)*diff(y(x),x)-y(x)^2-x*(x-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{c_{1} x -c_{1}+1} \]
✓ Solution by Mathematica
Time used: 0.202 (sec). Leaf size: 25
DSolve[x^2*(x-1)*y'[x]-y[x]^2-x*(x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{c_1 (-x)+1+c_1} \\ y(x)\to 0 \\ \end{align*}