69.6.26 problem 159

Internal problem ID [18069]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 159
Date solved : Thursday, October 02, 2025 at 02:36:59 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 19

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

\[ y = \ln \left (\frac {x^{3}}{\operatorname {LambertW}\left (\frac {x^{3}}{c_1}\right )}\right ) \]

✓ Mathematica. Time used: 3.763 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to W\left (e^{-c_1} x^3\right )+c_1 \end{align*}

✓ Sympy. Time used: 0.475 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} + W\left (x^{3} e^{- C_{1}}\right ) \]