60.1.548 problem 561

Internal problem ID [10562]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 561
Date solved : Sunday, March 30, 2025 at 06:05:40 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 1.288 (sec). Leaf size: 42

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

\[ y = x \cot \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\int _{}^{x^{2} \csc \left (\textit {\_Z} \right )^{2}}\frac {f \left (\textit {\_a} \right )}{\sqrt {-f \left (\textit {\_a} \right )^{2}+\textit {\_a}}\, \textit {\_a}}d \textit {\_a} +2 c_1 \right )\right ) \]

✓ Mathematica. Time used: 2.706 (sec). Leaf size: 2138

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

Too large to display

✗ Sympy

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

Timed Out