62.12.6 problem Ex 6

Internal problem ID [12852]
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 6
Date solved : Tuesday, January 28, 2025 at 04:27:23 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.135 (sec). Leaf size: 37

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]-1}{K[1]}dK[1]\&\right ][-x+\log (x)+c_1] \\ y(x)\to 0 \\ \end{align*}