Internal problem ID [4562]
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]
\[ \boxed {y y^{\prime } x +y^{2}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (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 \left (x \right ) = -\frac {\sqrt {-2 x^{4}+4 c_{1}}}{2 x} y \left (x \right ) = \frac {\sqrt {-2 x^{4}+4 c_{1}}}{2 x} \end{align*}
✓ Solution by Mathematica
Time used: 0.211 (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*}