60.2.136 problem 712

Internal problem ID [10710]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 712
Date solved : Sunday, March 30, 2025 at 06:25:01 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=\frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \end{align*}

✓ Maple. Time used: 0.170 (sec). Leaf size: 38

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

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

✓ Mathematica. Time used: 1.324 (sec). Leaf size: 49

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*x**3*sqrt(x**2 + 2*x - 4*y(x) + 1) + x**2 + 2*x + 1)/(2*x + 2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out