83.5.5 problem 1 (e)

Internal problem ID [21940]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. VI at page 47
Problem number : 1 (e)
Date solved : Sunday, October 12, 2025 at 05:51:37 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 3.546 (sec). Leaf size: 28

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

\[ \arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )-\frac {x^{2}}{2}-c_{1} = 0 \]

✓ Mathematica. Time used: 0.212 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to -x \cos \left (\frac {1}{2} \left (x^2-2 i c_1\right )\right ) \end{align*}

✗ Sympy

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

Timed Out