62.12.7 problem Ex 7

Internal problem ID [12853]
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
Date solved : Tuesday, January 28, 2025 at 04:27:24 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y-x \right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 17

dsolve((y(x)-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 2.702 (sec). Leaf size: 27

DSolve[(y[x]-x)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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