12.18 problem Ex 19

Internal problem ID [10170]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number: Ex 19.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]

\[ \boxed {y^{2} x +y-y^{\prime } x=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 18

dsolve((x*y(x)^2+y(x))-x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {2 x}{-x^{2}+2 c_{1}} \]

Solution by Mathematica

Time used: 0.136 (sec). Leaf size: 23

DSolve[(x*y[x]^2+y[x])-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*}