6.41 problem Exercise 12.41, page 103

Internal problem ID [4054]

Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number: Exercise 12.41, page 103.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]

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

Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

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

\begin{align*} y \relax (x ) = -\frac {\sqrt {-2 x^{4}+4 c_{1}}}{2 x} \\ y \relax (x ) = \frac {\sqrt {-2 x^{4}+4 c_{1}}}{2 x} \\ \end{align*}

Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 46

DSolve[x*y[x]*y'[x]+x^2+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-\frac {x^4}{2}+c_1}}{x} \\ y(x)\to \frac {\sqrt {-\frac {x^4}{2}+c_1}}{x} \\ \end{align*}