88.8.7 problem 7

Internal problem ID [24015]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 44
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:54:11 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 49

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (9 \textit {\_Z}^{3} {\mathrm e}^{3 \textit {\_Z}}-9 \,{\mathrm e}^{3 \textit {\_Z}} \textit {\_Z}^{2}+9 \textit {\_Z}^{2} x^{3}+12 \,{\mathrm e}^{3 \textit {\_Z}} \textit {\_Z} -4 \,{\mathrm e}^{3 \textit {\_Z}}+9 c_1 \right )} \]

✓ Mathematica. Time used: 0.131 (sec). Leaf size: 56

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

\[ \text {Solve}\left [x^3 \log ^2(y(x))-\frac {4 y(x)^3}{9}+y(x)^3 \log ^3(y(x))-y(x)^3 \log ^2(y(x))+\frac {4}{3} y(x)^3 \log (y(x))=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.942 (sec). Leaf size: 63

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

\[ C_{1} + \frac {x^{3} \log {\left (y{\left (x \right )} \right )}^{2}}{3} + \frac {y^{3}{\left (x \right )} \log {\left (y{\left (x \right )} \right )}^{3}}{3} - \frac {y^{3}{\left (x \right )} \log {\left (y{\left (x \right )} \right )}^{2}}{3} + \frac {4 y^{3}{\left (x \right )} \log {\left (y{\left (x \right )} \right )}}{9} - \frac {4 y^{3}{\left (x \right )}}{27} = 0 \]