89.2.11 problem 11

Internal problem ID [24276]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 27
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:05:45 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {\sqrt {-2 x^{4}+4 c_1}}{2 x} \\ y &= \frac {\sqrt {-2 x^{4}+4 c_1}}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 46

ode=(x^2+y[x]^2)+x*y[x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.246 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 + x*y(x)*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} - 2 x^{4}}}{2 x}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} - 2 x^{4}}}{2 x}\right ] \]