29.19.7 problem 520

Internal problem ID [5116]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 520
Date solved : Monday, January 27, 2025 at 10:12:09 AM
CAS classification : [_separable]

\begin{align*} x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 15

dsolve(x*(1-y(x))*diff(y(x),x)+(1-x)*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.760 (sec). Leaf size: 26

DSolve[x(1-y[x])D[y[x],x]+(1-x)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -W\left (-\frac {e^{x-c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}