54.2.382 problem 961

Internal problem ID [12256]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 961
Date solved : Wednesday, October 01, 2025 at 01:24:01 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }&=\frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}} \end{align*}

✓ Maple. Time used: 0.070 (sec). Leaf size: 44

ode:=diff(y(x),x) = (y(x)^2+2*x*y(x)+x^2+exp(2+2*y(x)^4-4*x^2*y(x)^2+2*x^4+2*y(x)^6-6*y(x)^4*x^2+6*x^4*y(x)^2-2*x^6))/(y(x)^2+2*x*y(x)+x^2-exp(2+2*y(x)^4-4*x^2*y(x)^2+2*x^4+2*y(x)^6-6*y(x)^4*x^2+6*x^4*y(x)^2-2*x^6)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-\textit {\_Z} +\int _{}^{{\mathrm e}^{\textit {\_Z}} \left ({\mathrm e}^{\textit {\_Z}}-2 x \right )}\frac {1}{{\mathrm e}^{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+2}+\textit {\_a}}d \textit {\_a} +c_1 \right )}-x \]

✓ Mathematica. Time used: 20.924 (sec). Leaf size: 813

ode=D[y[x],x] == (E^(2 + 2*x^4 - 2*x^6 - 4*x^2*y[x]^2 + 6*x^4*y[x]^2 + 2*y[x]^4 - 6*x^2*y[x]^4 + 2*y[x]^6) + x^2 + 2*x*y[x] + y[x]^2)/(-E^(2 + 2*x^4 - 2*x^6 - 4*x^2*y[x]^2 + 6*x^4*y[x]^2 + 2*y[x]^4 - 6*x^2*y[x]^4 + 2*y[x]^6) + x^2 + 2*x*y[x] + y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^x\left (\frac {1}{K[1]+y(x)}-\frac {2 e^{2 K[1]^6+6 y(x)^4 K[1]^2+4 y(x)^2 K[1]^2} K[1]}{e^{2 K[1]^6+6 y(x)^4 K[1]^2+4 y(x)^2 K[1]^2} K[1]^2-e^{2 y(x)^6+2 y(x)^4+6 K[1]^4 y(x)^2+2 K[1]^4+2}-e^{2 K[1]^6+6 y(x)^4 K[1]^2+4 y(x)^2 K[1]^2} y(x)^2}\right )dK[1]+\int _1^{y(x)}\left (-\frac {2 e^{2 x^6+6 K[2]^4 x^2+4 K[2]^2 x^2} K[2]}{-e^{2 x^6+6 K[2]^4 x^2+4 K[2]^2 x^2} x^2+e^{2 K[2]^6+2 K[2]^4+6 x^4 K[2]^2+2 x^4+2}+e^{2 x^6+6 K[2]^4 x^2+4 K[2]^2 x^2} K[2]^2}-\int _1^x\left (-\frac {2 e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[1] \left (24 K[1]^2 K[2]^3+8 K[1]^2 K[2]\right )}{e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[1]^2-e^{2 K[2]^6+2 K[2]^4+6 K[1]^4 K[2]^2+2 K[1]^4+2}-e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[2]^2}+\frac {2 e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[1] \left (e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} \left (24 K[1]^2 K[2]^3+8 K[1]^2 K[2]\right ) K[1]^2-2 e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[2]-e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[2]^2 \left (24 K[1]^2 K[2]^3+8 K[1]^2 K[2]\right )-e^{2 K[2]^6+2 K[2]^4+6 K[1]^4 K[2]^2+2 K[1]^4+2} \left (12 K[2]^5+8 K[2]^3+12 K[1]^4 K[2]\right )\right )}{\left (e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[1]^2-e^{2 K[2]^6+2 K[2]^4+6 K[1]^4 K[2]^2+2 K[1]^4+2}-e^{2 K[1]^6+6 K[2]^4 K[1]^2+4 K[2]^2 K[1]^2} K[2]^2\right )^2}-\frac {1}{(K[1]+K[2])^2}\right )dK[1]+\frac {1}{x+K[2]}\right )dK[2]=c_1,y(x)\right ] \]

✗ 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**6 + 6*x**4*y(x)**2 + 2*x**4 - 6*x**2*y(x)**4 - 4*x**2*y(x)**2 + 2*y(x)**6 + 2*y(x)**4 + 2))/(x**2 + 2*x*y(x) + y(x)**2 - exp(-2*x**6 + 6*x**4*y(x)**2 + 2*x**4 - 6*x**2*y(x)**4 - 4*x**2*y(x)**2 + 2*y(x)**6 + 2*y(x)**4 + 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out