42.4.1 problem Problem 3.1

Internal problem ID [8829]
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 3.1
Date solved : Tuesday, September 30, 2025 at 05:53:00 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \end{align*}

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

ode:=y(x)+(x^2+y(x)^2)^(1/2)-x*diff(y(x),x) = 0; 
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]+Sqrt[x^2+y[x]^2]-x*D[y[x],x]==0; 
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: 0.726 (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)
 

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