Internal problem ID [10159]
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`]]
\[ \boxed {\left (-x +y\right ) y^{\prime }+y=0} \]
✓ 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)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {LambertW}\left (-x \,{\mathrm e}^{-c_{1}}\right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 3.975 (sec). Leaf size: 25
DSolve[(y[x]-x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{W\left (-e^{-c_1} x\right )+c_1} \\ y(x)\to 0 \\ \end{align*}