40.4.6 problem 19 (g)

Internal problem ID [6646]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (g)
Date solved : Monday, January 27, 2025 at 02:16:41 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

\begin{align*} y+\left (y x +x -3 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 34

dsolve(y(x)+(x*y(x)+x-3*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {-3+\left (x -3\right ) \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {3}{x -3}}}{c_1 \left (x -3\right )}\right )}{x -3} \]

✓ Solution by Mathematica

Time used: 60.046 (sec). Leaf size: 31

DSolve[y[x]+(x*y[x]+x-3*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {3}{x-3}+W\left (\frac {c_1 e^{\frac {3}{x-3}}}{x-3}\right ) \]