Internal problem ID [5303]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]
\[ \boxed {y+\left (x y+x -3 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
dsolve(y(x)+(x*y(x)+x-3*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-3+\left (x -3\right ) \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {3}{x -3}}}{c_{1} \left (x -3\right )}\right )}{x -3} \]
✓ Solution by Mathematica
Time used: 60.04 (sec). Leaf size: 31
DSolve[y[x]+(x*y[x]+x-3*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {3}{x-3}+W\left (\frac {c_1 e^{\frac {3}{x-3}}}{x-3}\right ) \]