29.24.32 problem 695

Internal problem ID [5285]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 695
Date solved : Sunday, March 30, 2025 at 07:51:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 27

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{3 \textit {\_Z}}+9 \,{\mathrm e}^{\textit {\_Z}}+3 c_1 +3 \textit {\_Z} +3 \ln \left (x \right )\right )} x \]

✓ Mathematica. Time used: 0.151 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 1.571 (sec). Leaf size: 29

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

\[ \log {\left (y{\left (x \right )} \right )} = C_{1} + \frac {\left (- \frac {9 x^{2}}{y^{2}{\left (x \right )}} - 1\right ) y^{3}{\left (x \right )}}{3 x^{3}} \]