32.4.14 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.6, page 90

Internal problem ID [5825]
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
Date solved : Monday, January 27, 2025 at 01:20:05 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.218 (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)
 

\[ 2 y \left (x \right )+\ln \left (-x +y \left (x \right )\right )-\ln \left (x +y \left (x \right )\right )-2 x -c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.347 (sec). Leaf size: 32

DSolve[(x^2-y[x]^2-y[x])-(x^2-y[x]^2-x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {e^{2 x-2 y(x)} (y(x)+x)}{2 (x-y(x))}=c_1,y(x)\right ] \]