60.2.156 problem 732

Internal problem ID [10730]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 732
Date solved : Sunday, March 30, 2025 at 06:27:54 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=\frac {-x^{2}-x -a x -a +2 x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 x +2} \end{align*}

✓ Maple. Time used: 0.249 (sec). Leaf size: 43

ode:=diff(y(x),x) = 1/2*(-x^2-x-a*x-a+2*x^3*(x^2+2*a*x+a^2+4*y(x))^(1/2))/(1+x); 
dsolve(ode,y(x), singsol=all);
 

\[ c_{1} +\frac {2 x^{3}}{3}-x^{2}+2 x -2 \ln \left (x +1\right )-\sqrt {x^{2}+2 a x +a^{2}+4 y} = 0 \]

✓ Mathematica. Time used: 1.639 (sec). Leaf size: 56

ode=D[y[x],x] == (-1/2*a - x/2 - (a*x)/2 - x^2/2 + x^3*Sqrt[a^2 + 2*a*x + x^2 + 4*y[x]])/(1 + x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} \left (-a^2-2 a x-x^2+\frac {1}{9} \left (-2 x^3+3 x^2-6 x+6 \log (-x-1)+6 c_1\right ){}^2\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (-a*x - a + 2*x**3*sqrt(a**2 + 2*a*x + x**2 + 4*y(x)) - x**2 - x)/(2*x + 2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out