23.1.255 problem 249

Internal problem ID [4862]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 249
Date solved : Tuesday, September 30, 2025 at 08:45:31 AM
CAS classification : [_rational, _Riccati]

\begin{align*} 3 x y^{\prime }&=3 x^{{2}/{3}}+\left (1-3 y\right ) y \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

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

\[ y = i \tan \left (-3 i x^{{1}/{3}}+c_1 \right ) x^{{1}/{3}} \]

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 79

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

\begin{align*} y(x)&\to \frac {\sqrt [3]{x} \left (i \cosh \left (3 \sqrt [3]{x}\right )+c_1 \sinh \left (3 \sqrt [3]{x}\right )\right )}{i \sinh \left (3 \sqrt [3]{x}\right )+c_1 \cosh \left (3 \sqrt [3]{x}\right )}\\ y(x)&\to \sqrt [3]{x} \tanh \left (3 \sqrt [3]{x}\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) + y(x)**2/x - y(x)/(3*x) - 1/x**(1/3) cannot be solved by the factorable group method