60.2.98 problem 674

Internal problem ID [10672]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 674
Date solved : Wednesday, March 05, 2025 at 12:18:09 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Maple. Time used: 0.216 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.648 (sec). Leaf size: 32

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

\[ y(x)\to -\frac {x^2}{4}+x+\log ^2(x+1)-2 c_1 \log (x+1)+c_1{}^2 \]

✓ Sympy. Time used: 1.389 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = - \frac {x^{2}}{4} + x + \left (C_{1} + \log {\left (x + 1 \right )}\right )^{2} \]