40.2.15 problem 40

Internal problem ID [6593]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 40
Date solved : Monday, January 27, 2025 at 02:14:50 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

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

\[ y = -\operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{x -1}}{x}\right )-1 \]

✓ Solution by Mathematica

Time used: 7.458 (sec). Leaf size: 29

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

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