Internal problem ID [10128]
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 12. Equations of
form \(y f_1(x y)+x f_2( xy) y'=0\). Page 18
Problem number: Ex 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y+y^{2} x +\left (x -x^{2} y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve((y(x)+x*y(x)^2)+(x-x^2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{\LambertW \left (-\frac {c_{1}}{x^{2}}\right ) x} \]
✓ Solution by Mathematica
Time used: 60.509 (sec). Leaf size: 30
DSolve[(y[x]+x*y[x]^2)+(x-x^2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x \text {ProductLog}\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^2}\right )} \\ \end{align*}