88.7.7 problem 7

Internal problem ID [24002]
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 41
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:52:03 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.153 (sec). Leaf size: 27

ode:=3*x^2*exp(x^3)+exp(2*y(x))+(2*x*exp(2*y(x))-3)*diff(y(x),x) = 0; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {\operatorname {LambertW}\left (-\frac {2 x \,{\mathrm e}^{\frac {2 \,{\mathrm e}^{x^{3}}}{3}-\frac {2}{3}}}{3}\right )}{2}+\frac {{\mathrm e}^{x^{3}}}{3}-\frac {1}{3} \]

✓ Mathematica. Time used: 3.958 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to \frac {1}{6} \left (-3 W\left (-\frac {2}{3} e^{\frac {2}{3} \left (e^{x^3}-1\right )} x\right )+2 e^{x^3}-2\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-3*x**2*exp(x**3) - exp(2*y(x)))/(2*x*exp