Internal problem ID [5250]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y y^{\prime }-\left (1+y\right ) \left (1-x \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(x*y(x)*diff(y(x),x)= (y(x)+1)*(1-x),y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{x -1}}{x}\right )-1 \]
✓ Solution by Mathematica
Time used: 6.202 (sec). Leaf size: 29
DSolve[x*y[x]*y'[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*}