1.5.28 problem 28

Internal problem ID [132]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 28
Date solved : Tuesday, September 30, 2025 at 03:45:35 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

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

\[ y = \ln \left (x^{2} \left ({\mathrm e}^{2 x}-c_1 \right )\right ) \]

✓ Mathematica. Time used: 3.895 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to \log \left (x^2 \left (e^{2 x}+c_1\right )\right ) \end{align*}

✗ Sympy

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

TypeError : NoneType object is not subscriptable