Internal problem ID [3973]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number: Recognizable Exact Differential equations. Integrating factors. Exercise 10.6,
page 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.563 (sec). Leaf size: 28
dsolve((x^2-y(x)^2-y(x))-(x^2-y(x)^2-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ 2 y \relax (x )+\ln \left (-x +y \relax (x )\right )-\ln \left (y \relax (x )+x \right )-2 x -c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.264 (sec). Leaf size: 32
DSolve[(x^2-y[x]^2-y[x])-(x^2-y[x]^2-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {e^{2 x-2 y(x)} (y(x)+x)}{2 (x-y(x))}=c_1,y(x)\right ] \]