60.1.358 problem 365

Internal problem ID [10372]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 365
Date solved : Sunday, March 30, 2025 at 04:30:32 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.053 (sec). Leaf size: 34

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

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

✓ Mathematica. Time used: 0.252 (sec). Leaf size: 156

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {x-f\left (x^2+K[2]^2\right ) K[2]}{x^2+K[2]^2}-\int _1^x\left (\frac {-2 K[1] K[2] f''\left (K[1]^2+K[2]^2\right )-1}{K[1]^2+K[2]^2}-\frac {2 \left (-f\left (K[1]^2+K[2]^2\right ) K[1]-K[2]\right ) K[2]}{\left (K[1]^2+K[2]^2\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {-f\left (K[1]^2+y(x)^2\right ) K[1]-y(x)}{K[1]^2+y(x)^2}dK[1]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out