Internal problem ID [3778]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 526.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x \left (x +y\right ) y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 44
dsolve(x*(x+y(x))*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1+\sqrt {c_{1} x^{2}+1}}{c_{1} x} y \left (x \right ) = -\frac {-1+\sqrt {c_{1} x^{2}+1}}{c_{1} x} \end{align*}
✓ Solution by Mathematica
Time used: 2.81 (sec). Leaf size: 80
DSolve[x(x+y[x])y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 c_1}-\sqrt {e^{2 c_1} \left (x^2+e^{2 c_1}\right )}}{x} y(x)\to \frac {\sqrt {e^{2 c_1} \left (x^2+e^{2 c_1}\right )}+e^{2 c_1}}{x} y(x)\to 0 \end{align*}