Internal problem ID [3689]
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`]]
\[ \boxed {\left (-y+x \right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve((x-y(x))*diff(y(x),x) = y(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {LambertW}\left (-x \,{\mathrm e}^{-c_{1}}\right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 4.105 (sec). Leaf size: 25
DSolve[(x-y[x])y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{W\left (-e^{-c_1} x\right )} y(x)\to 0 \end{align*}