Internal problem ID [3843]
Book: Differential and integral calculus, vol II By N. Piskunov. 1974
Section: Chapter 1
Problem number: Example, page 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y+x y^{2}-y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve((y(x)+x*y(x)^2)-x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x}{-x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.155 (sec). Leaf size: 23
DSolve[(y[x]+x*y[x]^2)-x*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*}