40.3.14 problem 24 (g)

Internal problem ID [6618]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 24 (g)
Date solved : Wednesday, March 05, 2025 at 01:33:12 AM
CAS classification : [_quadrature]

\begin{align*} 1-\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 24

ode=1-(Sqrt[a^2-x^2])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.664 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-sqrt(a**2 - x**2)*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \begin {cases} - i \log {\left (- 2 x + 2 i \sqrt {a^{2} - x^{2}} \right )} & \text {for}\: a^{2} \neq 0 \\\frac {x \log {\left (x \right )}}{\sqrt {- x^{2}}} & \text {otherwise} \end {cases} \]