62.11.2 problem Ex 2

Internal problem ID [12844]
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 18. Transformation of variables. Page 26
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:26:45 AM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} \left (x +y\right ) y^{\prime }-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve((x+y(x))*diff(y(x),x)-1=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 35

DSolve[(x+y[x])*D[y[x],x]-1==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=e^{y(x)} \int _1^{y(x)}e^{-K[1]} K[1]dK[1]+c_1 e^{y(x)},y(x)\right ] \]