32.6.10 problem Exercise 12.10, page 103

Internal problem ID [5875]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.10, page 103
Date solved : Tuesday, March 04, 2025 at 11:50:48 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.085 (sec). Leaf size: 18

ode:=y(x)+(1+y(x)^2*exp(2*x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 3.331 (sec). Leaf size: 57

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

\begin{align*} y(x)\to -\frac {e^{-x}}{\sqrt {W\left (e^{-2 x+2 c_1}\right )}} \\ y(x)\to \frac {e^{-x}}{\sqrt {W\left (e^{-2 x+2 c_1}\right )}} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((y(x)**2*exp(2*x) + 1)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : NoneType object is not subscriptable