29.23.26 problem 657

Internal problem ID [5248]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 657
Date solved : Sunday, March 30, 2025 at 07:30:58 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime }&=6 y^{3} \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 31

ode:=x*(x^3-3*x^3*y(x)+4*y(x)^2)*diff(y(x),x) = 6*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-3 \,{\mathrm e}^{\textit {\_Z}} x^{3}+6 c_1 \,x^{3}+\textit {\_Z} \,x^{3}+2 \,{\mathrm e}^{2 \textit {\_Z}}\right )} \]

✓ Mathematica. Time used: 0.156 (sec). Leaf size: 27

ode=x(x^3-3 x^3 y[x]+4 y[x]^2)D[y[x],x]==6 y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {y(x)^2}{x^3}+\frac {1}{2} (\log (y(x))-3 y(x))=c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.733 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(-3*x**3*y(x) + x**3 + 4*y(x)**2)*Derivative(y(x), x) - 6*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + \frac {y{\left (x \right )}}{2} - \frac {\log {\left (y{\left (x \right )} \right )}}{6} - \frac {y^{2}{\left (x \right )}}{3 x^{3}} = 0 \]