54.2.138 problem 715

Internal problem ID [12012]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 715
Date solved : Sunday, October 12, 2025 at 02:10:22 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Maple. Time used: 0.235 (sec). Leaf size: 39

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

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

✓ Mathematica. Time used: 1.053 (sec). Leaf size: 50

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

\begin{align*} 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+4 x\right ) \end{align*}

✗ Sympy

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

Timed Out