32.4.25 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.17, page 90

Internal problem ID [5836]
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 10.17, page 90
Date solved : Monday, January 27, 2025 at 01:20:15 PM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 36

dsolve((y(x))-(y(x)^2+x^2+x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \frac {{\mathrm e}^{-2 i y \left (x \right )} \left (i x +y \left (x \right )\right )+2 \left (i y \left (x \right )+x \right ) c_{1}}{2 i y \left (x \right )+2 x} = 0 \]

✓ Solution by Mathematica

Time used: 0.117 (sec). Leaf size: 18

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

\[ \text {Solve}\left [y(x)-\arctan \left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]