60.1.524 problem 537

Internal problem ID [10538]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 537
Date solved : Sunday, March 30, 2025 at 05:48:39 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y&=0 \end{align*}

✗ Maple

ode:=x^3*diff(y(x),x)^3-3*x^2*y(x)*diff(y(x),x)^2+(3*x*y(x)^2+x^6)*diff(y(x),x)-y(x)^3-2*x^5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 15

ode=-2*x^5*y[x] - y[x]^3 + (x^6 + 3*x*y[x]^2)*D[y[x],x] - 3*x^2*y[x]*D[y[x],x]^2 + x^3*D[y[x],x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 x \left (x+c_1{}^2\right ) \]

✗ Sympy

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

Timed Out