29.19.24 problem 537

Internal problem ID [5133]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 537
Date solved : Monday, January 27, 2025 at 10:13:45 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 7.140 (sec). Leaf size: 28

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

\begin{align*} y(x)\to 1+W\left (\frac {e^{-x-1+c_1}}{x-1}\right ) \\ y(x)\to 1 \\ \end{align*}