83.3.2 problem 1 (b)

Internal problem ID [21921]
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. IV at page 38
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 08:09:40 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 26

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

\[ \frac {-c_1 \,x^{2}+\sqrt {x^{2}+y^{2}}+y}{x^{2}} = 0 \]

✓ Mathematica. Time used: 0.173 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to x \sinh (\log (x)+c_1) \end{align*}

✓ Sympy. Time used: 0.728 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = - x \sinh {\left (C_{1} - \log {\left (x \right )} \right )} \]