15.2.7 problem 7

Internal problem ID [2877]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 7
Date solved : Sunday, March 30, 2025 at 12:38:06 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.397 (sec). Leaf size: 16

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

\[ y(x)\to -x \cosh (-\log (x)+c_1) \]

✓ Sympy. Time used: 1.379 (sec). Leaf size: 10

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)
 

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