54.2.252 problem 829

Internal problem ID [12126]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 829
Date solved : Sunday, October 12, 2025 at 02:21:45 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}} \end{align*}

✓ Maple. Time used: 0.246 (sec). Leaf size: 41

ode:=diff(y(x),x) = 1/2*(1+2*(4*x^2*y(x)+1)^(1/2)*x^3+2*x^5*(4*x^2*y(x)+1)^(1/2)+2*x^6*(4*x^2*y(x)+1)^(1/2))/x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {4 x^{6}+5 x^{5}+10 x^{3}+10 c_{1} x -10 \sqrt {4 x^{2} y+1}}{10 x} = 0 \]

✓ Mathematica. Time used: 0.328 (sec). Leaf size: 4509

ode=D[y[x],x] == (1/2 + x^3*Sqrt[1 + 4*x^2*y[x]] + x^5*Sqrt[1 + 4*x^2*y[x]] + x^6*Sqrt[1 + 4*x^2*y[x]])/x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*x**6*sqrt(4*x**2*y(x) + 1) + 2*x**5*sqrt(4*x**2*y(x) + 1) + 2*x**3*sqrt(4*x**2*y(x) + 1) + 1)/(2*x**3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out