Internal problem ID [5240]
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: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x y^{2}+y+\left (y x^{2}-x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve((x*y(x)^2+y(x))+(x^2*y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = x \,{\mathrm e}^{-\operatorname {LambertW}\left (-x^{2} {\mathrm e}^{-2 c_{1}}\right )-2 c_{1}} \]
✓ Solution by Mathematica
Time used: 13.386 (sec). Leaf size: 33
DSolve[(x*y[x]^2+y[x])+(x^2*y[x]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {W\left (e^{-1+\frac {9 c_1}{2^{2/3}}} x^2\right )}{x} y(x)\to 0 \end{align*}