29.25.14 problem 711

Internal problem ID [5301]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 711
Date solved : Sunday, March 30, 2025 at 07:52:14 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.214 (sec). Leaf size: 160

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

\[ y = \frac {x \left (c_1 x -a \operatorname {RootOf}\left (a^{2} \textit {\_Z}^{4}-2 a x c_1 \,\textit {\_Z}^{3}+\left (a^{2} x^{2} c_1^{2}+b^{2} x^{2} c_1^{2}+x^{2} c_1^{2}-b^{2}\right ) \textit {\_Z}^{2}-2 a \,x^{3} c_1^{3} \textit {\_Z} +x^{4} c_1^{4}\right )\right )}{b \operatorname {RootOf}\left (a^{2} \textit {\_Z}^{4}-2 a x c_1 \,\textit {\_Z}^{3}+\left (a^{2} x^{2} c_1^{2}+b^{2} x^{2} c_1^{2}+x^{2} c_1^{2}-b^{2}\right ) \textit {\_Z}^{2}-2 a \,x^{3} c_1^{3} \textit {\_Z} +x^{4} c_1^{4}\right )} \]

✓ Mathematica. Time used: 61.819 (sec). Leaf size: 13289

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

Too large to display

✗ Sympy

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

Timed Out