Internal problem ID [10163]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary.
Page 29
Problem number: Ex 7.
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 (y-x \right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve((y(x)-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\LambertW \left (-x \,{\mathrm e}^{-c_{1}}\right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 60.022 (sec). Leaf size: 20
DSolve[(y[x]-x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\text {ProductLog}\left (-e^{-c_1} x\right )+c_1} \\ \end{align*}