54.2.235 problem 812

Internal problem ID [12109]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 812
Date solved : Sunday, October 12, 2025 at 02:18:21 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=\frac {x^{2}}{2}+\sqrt {x^{3}-6 y}+x^{2} \sqrt {x^{3}-6 y}+x^{3} \sqrt {x^{3}-6 y} \end{align*}

✓ Maple. Time used: 0.212 (sec). Leaf size: 30

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

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

✓ Mathematica. Time used: 0.399 (sec). Leaf size: 76

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

\begin{align*} y(x)&\to -\frac {3 x^8}{32}-\frac {x^7}{4}-\frac {x^6}{6}-\frac {3 x^5}{4}+\left (-1+\frac {3 c_1}{4}\right ) x^4+\left (\frac {1}{6}+c_1\right ) x^3-\frac {3 x^2}{2}+3 c_1 x-\frac {3 c_1{}^2}{2} \end{align*}

✗ Sympy

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

Timed Out