Internal problem ID [5327]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
198
Problem number: 1(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x^{2}+y x +\left (x +y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve((x^2+x*y(x))+(x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x \\ y \relax (x ) = -\frac {x^{2}}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.202 (sec). Leaf size: 53
DSolve[(x^2+y[x])+(x+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\sqrt {-\frac {2 x^3}{3}+x^2+c_1} \\ y(x)\to -x+\sqrt {-\frac {2 x^3}{3}+x^2+c_1} \\ \end{align*}