60.2.270 problem 847

Internal problem ID [10844]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 847
Date solved : Sunday, March 30, 2025 at 07:12:55 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Maple. Time used: 0.206 (sec). Leaf size: 34

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

\[ c_{1} -\frac {x^{4}}{2}-\frac {2 x^{3}}{3}-2 x -\sqrt {x^{2}+2 x +1-4 y} = 0 \]

✓ Mathematica. Time used: 0.751 (sec). Leaf size: 69

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

\[ y(x)\to \frac {1}{144} \left (-9 x^8-24 x^7-16 x^6-72 x^5+24 (-4+3 c_1) x^4+96 c_1 x^3-108 x^2+72 (1+4 c_1) x+36-144 c_1{}^2\right ) \]

✗ Sympy

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

Timed Out