81.1.12 problem 2-11

Internal problem ID [21457]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-11
Date solved : Thursday, October 02, 2025 at 07:38:32 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-\frac {x}{y} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=diff(y(x),x) = -x/y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 39

ode=D[y[x],x]==-x/y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.135 (sec). Leaf size: 22

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

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