32.6.41 problem Exercise 12.41, page 103

Internal problem ID [5906]
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
Date solved : Monday, January 27, 2025 at 01:25:36 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.007 (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: 0.232 (sec). Leaf size: 46

DSolve[x*y[x]*D[y[x],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*}