89.1.21 problem 21

Internal problem ID [24256]
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 21
Problem number : 21
Date solved : Thursday, October 02, 2025 at 10:02:11 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

ode:=x+(a^2-x^2)^(1/2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (a -x \right ) \left (a +x \right )}{\sqrt {a^{2}-x^{2}}}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 21

ode=(x)+Sqrt[a^2-x^2]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.535 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} + \sqrt {- \left (- a + x\right ) \left (a + x\right )} \]