54.2.49 problem 625

Internal problem ID [11923]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 625
Date solved : Sunday, October 12, 2025 at 02:02:53 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.063 (sec). Leaf size: 55

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

\[ i \ln \left (-x^{3}+6 y+1\right )+2 \sqrt {-x^{3}+6 y}-2 \arctan \left (\sqrt {-x^{3}+6 y}\right )+2 i x^{3}-c_1 = 0 \]

✓ Mathematica. Time used: 3.782 (sec). Leaf size: 69

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

\begin{align*} y(x)&\to \frac {1}{6} \left (-W\left (-i e^{-x^3-1-6 c_1}\right ){}^2-2 W\left (-i e^{-x^3-1-6 c_1}\right )+x^3-1\right )\\ y(x)&\to \frac {1}{6} \left (x^3-1\right ) \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded