56.12.25 problem Ex 26

Internal problem ID [14152]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 26
Date solved : Thursday, October 02, 2025 at 09:17:31 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+y^{2}\right ) \left (y y^{\prime }+x \right )+\sqrt {1+x^{2}+y^{2}}\, \left (y-x y^{\prime }\right )&=0 \end{align*}

✓ Maple. Time used: 0.044 (sec). Leaf size: 25

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

\[ \arctan \left (\frac {x}{y}\right )+\sqrt {1+x^{2}+y^{2}}-c_1 = 0 \]

✓ Mathematica. Time used: 0.187 (sec). Leaf size: 27

ode=(x^2+y[x]^2)*(x+y[x]*D[y[x],x])+(1+x^2+y[x]^2)^(1/2)*(y[x]-x*D[y[x],x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\arctan \left (\frac {x}{y(x)}\right )+\sqrt {x^2+y(x)^2+1}=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + y(x)*Derivative(y(x), x))*(x**2 + y(x)**2) + (-x*Derivative(y(x), x) + y(x))*sqrt(x**2 + y(x)**2 + 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out