54.2.313 problem 892

Internal problem ID [12187]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 892
Date solved : Wednesday, October 01, 2025 at 01:07:56 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }&=\frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}} \end{align*}

✓ Maple. Time used: 0.165 (sec). Leaf size: 39

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-\textit {\_Z} +\int _{}^{{\mathrm e}^{\textit {\_Z}} \left ({\mathrm e}^{\textit {\_Z}}-2 x \right )}\frac {1}{{\mathrm e}^{\frac {2}{\textit {\_a} +1}}+\textit {\_a}}d \textit {\_a} +c_1 \right )}-x \]

✓ Mathematica. Time used: 1.047 (sec). Leaf size: 1283

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out