71.6.15 problem 15

Internal problem ID [14421]
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
Date solved : Tuesday, January 28, 2025 at 06:30:29 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {y^{2}}{1-y x} \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 17

dsolve(diff(y(x),x)=y(x)^2/(1-x*y(x)),y(x), singsol=all)
 

\[ y = -\frac {\operatorname {LambertW}\left (-x \,{\mathrm e}^{-c_{1}}\right )}{x} \]

✓ Solution by Mathematica

Time used: 1.975 (sec). Leaf size: 25

DSolve[D[y[x],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*}