83.8.6 problem 6

Internal problem ID [19061]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 6
Date solved : Monday, March 31, 2025 at 06:42:49 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 15.063 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.236 (sec). Leaf size: 12

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

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

✗ Sympy

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

Timed Out