Internal problem ID [12325]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {x y}{1-y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x)=x*y(x)/(1-y(x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-{\mathrm e}^{\frac {x^{2}}{2}+c_{1}}\right )+\frac {x^{2}}{2}+c_{1}} \]
✓ Solution by Mathematica
Time used: 3.96 (sec). Leaf size: 29
DSolve[y'[x]==x*y[x]/(1-y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -W\left (-e^{\frac {x^2}{2}-c_1}\right ) y(x)\to 0 \end{align*}