29.15.27 problem 435

Internal problem ID [5033]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 435
Date solved : Monday, January 27, 2025 at 10:04:54 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 4.004 (sec). Leaf size: 27

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

\begin{align*} y(x)\to -\frac {x}{W\left (-e^{-1-c_1} x\right )} \\ y(x)\to 0 \\ \end{align*}