29.25.10 problem 707

Internal problem ID [5297]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 707
Date solved : Tuesday, March 04, 2025 at 09:16:41 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.127 (sec). Leaf size: 25

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

\[ y \left (x \right ) = \operatorname {RootOf}\left (x^{9} \textit {\_Z}^{4}+3-{\mathrm e}^{\frac {9 c_{1}}{4}} \textit {\_Z} \right ) x^{3} \]

✓ Mathematica. Time used: 60.135 (sec). Leaf size: 1021

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

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

✓ Sympy. Time used: 2.181 (sec). Leaf size: 1034

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

\[ \text {Solution too large to show} \]