Internal problem ID [3984]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y-\left (x +x^{2}+y^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 30
dsolve((y(x))-(y(x)^2+x^2+x)*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1}+\frac {{\mathrm e}^{-2 i y \relax (x )} \left (i x +y \relax (x )\right )}{2 i y \relax (x )+2 x} = 0 \]
✓ Solution by Mathematica
Time used: 0.103 (sec). Leaf size: 18
DSolve[(y[x])-(y[x]^2+x^2+x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)-\text {ArcTan}\left (\frac {x}{y(x)}\right )=c_1,y(x)\right ] \]