8.5.28 problem 28

Internal problem ID [756]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 28
Date solved : Saturday, March 29, 2025 at 10:19:56 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

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

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

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

✓ Mathematica. Time used: 4.266 (sec). Leaf size: 18

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

\[ y(x)\to \log \left (x^2 \left (e^{2 x}+c_1\right )\right ) \]

✗ 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