23.1.640 problem 634

Internal problem ID [5247]
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 : 634
Date solved : Tuesday, September 30, 2025 at 12:00:10 PM
CAS classification : [_exact, _rational]

\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }+x^{2}-3 x y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 769

ode:=(1-3*x^2*y(x)+6*y(x)^2)*diff(y(x),x)+x^2-3*x*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 9.625 (sec). Leaf size: 570

ode=(1-3*x^2*y[x]+6*y[x]^2)*D[y[x],x]+x^2-3*x*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^2}{4}-\frac {\sqrt [3]{-\frac {27 x^6}{4}+36 x^3+27 x^2+\sqrt {4 \left (6-\frac {9 x^4}{4}\right )^3+\left (-\frac {27 x^6}{4}+36 x^3+27 x^2+108 c_1\right ){}^2}+108 c_1}}{6 \sqrt [3]{2}}+\frac {6-\frac {9 x^4}{4}}{3\ 2^{2/3} \sqrt [3]{-\frac {27 x^6}{4}+36 x^3+27 x^2+\sqrt {4 \left (6-\frac {9 x^4}{4}\right )^3+\left (-\frac {27 x^6}{4}+36 x^3+27 x^2+108 c_1\right ){}^2}+108 c_1}}\\ y(x)&\to \frac {x^2}{4}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-\frac {27 x^6}{4}+36 x^3+27 x^2+\sqrt {4 \left (6-\frac {9 x^4}{4}\right )^3+\left (-\frac {27 x^6}{4}+36 x^3+27 x^2+108 c_1\right ){}^2}+108 c_1}}{12 \sqrt [3]{2}}-\frac {\left (1+i \sqrt {3}\right ) \left (6-\frac {9 x^4}{4}\right )}{6\ 2^{2/3} \sqrt [3]{-\frac {27 x^6}{4}+36 x^3+27 x^2+\sqrt {4 \left (6-\frac {9 x^4}{4}\right )^3+\left (-\frac {27 x^6}{4}+36 x^3+27 x^2+108 c_1\right ){}^2}+108 c_1}}\\ y(x)&\to \frac {x^2}{4}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-\frac {27 x^6}{4}+36 x^3+27 x^2+\sqrt {4 \left (6-\frac {9 x^4}{4}\right )^3+\left (-\frac {27 x^6}{4}+36 x^3+27 x^2+108 c_1\right ){}^2}+108 c_1}}{12 \sqrt [3]{2}}-\frac {\left (1-i \sqrt {3}\right ) \left (6-\frac {9 x^4}{4}\right )}{6\ 2^{2/3} \sqrt [3]{-\frac {27 x^6}{4}+36 x^3+27 x^2+\sqrt {4 \left (6-\frac {9 x^4}{4}\right )^3+\left (-\frac {27 x^6}{4}+36 x^3+27 x^2+108 c_1\right ){}^2}+108 c_1}} \end{align*}

✗ Sympy

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

Timed Out