15.27 problem 435

Internal problem ID [3181]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 15
Problem number: 435.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]

Solve \begin {gather*} \boxed {\left (x -y\right ) y^{\prime }-y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

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

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

Solution by Mathematica

Time used: 60.024 (sec). Leaf size: 20

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

\begin{align*} y(x)\to e^{\text {ProductLog}\left (-e^{-c_1} x\right )+c_1} \\ \end{align*}