Internal problem ID [5252]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 42.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y \left (1+2 y x \right )+x \left (1-y x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(y(x)*(1+2*x*y(x))+x*(1-x*y(x))*diff(y(x),x)= 0,y(x), singsol=all)
\[ y = -\frac {1}{\operatorname {LambertW}\left (-\frac {c_{1}}{x^{3}}\right ) x} \]
✓ Solution by Mathematica
Time used: 6.645 (sec). Leaf size: 35
DSolve[y[x]*(1+2*x*y[x])+x*(1-x*y[x])*y'[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x W\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^3}\right )} y(x)\to 0 \end{align*}