78.8.4 problem 4

Internal problem ID [18123]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 4
Date solved : Thursday, March 13, 2025 at 11:38:23 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 51

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

\[ \frac {y^{2}+\sqrt {x^{2}+y^{2}}\, y+\left (\ln \left (y+\sqrt {x^{2}+y^{2}}\right )-c_{1} -3 \ln \left (x \right )\right ) x^{2}}{x^{2}} = 0 \]

✓ Mathematica. Time used: 0.26 (sec). Leaf size: 66

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

\[ \text {Solve}\left [\frac {1}{2} \left (\frac {y(x) \left (\sqrt {\frac {y(x)^2}{x^2}+1}+\frac {y(x)}{x}\right )}{x}-\log \left (\sqrt {\frac {y(x)^2}{x^2}+1}-\frac {y(x)}{x}\right )\right )=\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

TypeError : cannot determine truth value of Relational