29.19.13 problem 526

Internal problem ID [5122]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 526
Date solved : Monday, January 27, 2025 at 10:12:21 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.095 (sec). Leaf size: 45

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: 2.961 (sec). Leaf size: 80

DSolve[x(x+y[x])D[y[x],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*}