60.1.299 problem 305

Internal problem ID [10313]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 305
Date solved : Sunday, March 30, 2025 at 03:58:54 PM
CAS classification : [_exact, _rational]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

\[ \frac {x^{3}}{3}-3 x y+\frac {y^{4}}{4}+c_1 = 0 \]

✓ Mathematica. Time used: 60.176 (sec). Leaf size: 1211

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out