29.17.3 problem 462

Internal problem ID [5060]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 462
Date solved : Monday, January 27, 2025 at 10:07:04 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x -2 y\right ) y^{\prime }&=y \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 17

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

\[ y \left (x \right ) = -\frac {x}{2 \operatorname {LambertW}\left (-\frac {x \,{\mathrm e}^{-\frac {c_{1}}{2}}}{2}\right )} \]

✓ Solution by Mathematica

Time used: 4.432 (sec). Leaf size: 33

DSolve[(x-2 y[x])D[y[x],x]==y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x}{2 W\left (-\frac {1}{2} e^{-1-\frac {c_1}{2}} x\right )} \\ y(x)\to 0 \\ \end{align*}