48.4.21 problem Problem 3.34

Internal problem ID [7563]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.34
Date solved : Sunday, March 30, 2025 at 12:15:27 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.087 (sec). Leaf size: 27

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

\[ y-\arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.456 (sec). Leaf size: 29

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

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

✗ Sympy

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

Timed Out