15.8.20 problem 20

Internal problem ID [3023]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 20
Date solved : Sunday, March 30, 2025 at 01:10:49 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 26

ode:=x*diff(y(x),x)-y(x)-(x^2+y(x)^2)^(1/2) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.312 (sec). Leaf size: 13

ode=x*D[y[x],x]-y[x]-Sqrt[x^2+y[x]^2]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x \sinh (\log (x)+c_1) \]

✓ Sympy. Time used: 1.133 (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)
 

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