60.2.72 problem 648

Internal problem ID [10646]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 648
Date solved : Sunday, March 30, 2025 at 06:14:47 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=-\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \end{align*}

✓ Maple. Time used: 0.724 (sec). Leaf size: 49

ode:=diff(y(x),x) = -1/2*x^3*(a^(1/2)*x+a^(1/2)-2*(a*x^4+8*y(x))^(1/2))*a^(1/2)/(1+x); 
dsolve(ode,y(x), singsol=all);
 

\[ -\sqrt {a \,x^{4}+8 y}-4 \sqrt {a}\, \ln \left (x +1\right )+\frac {2 \left (2 x^{3}-3 x^{2}+6 x \right ) \sqrt {a}}{3}-c_{1} = 0 \]

✓ Mathematica. Time used: 4.313 (sec). Leaf size: 53

ode=D[y[x],x] == -1/2*(Sqrt[a]*x^3*(Sqrt[a] + Sqrt[a]*x - 2*Sqrt[a*x^4 + 8*y[x]]))/(1 + x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {a x^4}{8}+2 a \left (\int \frac {x^3}{x+1} \, dx\right )^2-4 a c_1 \int \frac {x^3}{x+1} \, dx+2 a c_1{}^2 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(sqrt(a)*x**3*(sqrt(a)*x + sqrt(a) - 2*sqrt(a*x**4 + 8*y(x)))/(2*x + 2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out