19.13 problem 526

Internal problem ID [3270]

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]]

Solve \begin {gather*} \boxed {x \left (x +y\right ) y^{\prime }+y^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.031 (sec). Leaf size: 44

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

\begin{align*} y \relax (x ) = \frac {1+\sqrt {c_{1} x^{2}+1}}{c_{1} x} \\ y \relax (x ) = -\frac {-1+\sqrt {c_{1} x^{2}+1}}{c_{1} x} \\ \end{align*}

Solution by Mathematica

Time used: 2.045 (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*}