7.5.12 problem 12

Internal problem ID [116]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 12
Date solved : Thursday, March 13, 2025 at 03:21:55 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y y^{\prime }&=y^{2}+x \sqrt {4 x^{2}+y^{2}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 30

ode:=x*y(x)*diff(y(x),x) = y(x)^2+x*(4*x^2+y(x)^2)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\ln \left (x \right ) x -c_1 x -\sqrt {4 x^{2}+y^{2}}}{x} = 0 \]

✓ Mathematica. Time used: 0.293 (sec). Leaf size: 54

ode=x*y[x]*D[y[x],x]==y[x]^2+x*Sqrt[4*x^2+y[x]^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -x \sqrt {\log ^2(x)+2 c_1 \log (x)-4+c_1{}^2} \\ y(x)\to x \sqrt {\log ^2(x)+2 c_1 \log (x)-4+c_1{}^2} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*sqrt(4*x**2 + y(x)**2) + x*y(x)*Derivative(y(x), x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : cannot determine truth value of Relational