Internal problem ID [12365]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{\prime }-\frac {y^{2}}{1-y x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)=y(x)^2/(1-x*y(x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-x \,{\mathrm e}^{-c_{1}}\right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 3.256 (sec). Leaf size: 25
DSolve[y'[x]==y[x]^2/(1-x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {W\left (-e^{-c_1} x\right )}{x} y(x)\to 0 \end{align*}