81.1.17 problem 2-15

Internal problem ID [21462]
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 : 2-15
Date solved : Saturday, October 04, 2025 at 05:35:39 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=a_{0} \\ \end{align*}

✗ Maple

ode:=diff(y(x),x) = -x/y(x); 
ic:=[y(0) = a__0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 37

ode=D[y[x],x]==-x/y[x]; 
ic={y[0]==a0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {\text {a0}^2-x^2}\\ y(x)&\to \sqrt {\text {a0}^2-x^2} \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
a0 = symbols("a0") 
y = Function("y") 
ode = Eq(x/y(x) + Derivative(y(x), x),0) 
ics = {y(0): a0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {a_{0}^{2} - x^{2}} \]