60.1.502 problem 515

Internal problem ID [10516]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 515
Date solved : Sunday, March 30, 2025 at 05:42:15 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.675 (sec). Leaf size: 132

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

\begin{align*} y &= -i x \\ y &= i x \\ y &= \operatorname {RootOf}\left (x^{2}+\textit {\_Z}^{2}-f \left (\textit {\_Z}^{2}+x^{2}\right )\right ) \\ y &= x \cot \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +2 c_1 -\int _{}^{x^{2} \csc \left (\textit {\_Z} \right )^{2}}\frac {\sqrt {f \left (\textit {\_a} \right ) \left (-f \left (\textit {\_a} \right )+\textit {\_a} \right )}}{\left (f \left (\textit {\_a} \right )-\textit {\_a} \right ) \textit {\_a}}d \textit {\_a} \right )\right ) \\ y &= x \cot \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\int _{}^{x^{2} \csc \left (\textit {\_Z} \right )^{2}}\frac {\sqrt {f \left (\textit {\_a} \right ) \left (-f \left (\textit {\_a} \right )+\textit {\_a} \right )}}{\left (f \left (\textit {\_a} \right )-\textit {\_a} \right ) \textit {\_a}}d \textit {\_a} +2 c_1 \right )\right ) \\ \end{align*}

✓ Mathematica. Time used: 2.796 (sec). Leaf size: 1922

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

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✗ Sympy

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

Timed Out