44.4.6 problem 2 (b)

Internal problem ID [7019]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 2 (b)
Date solved : Sunday, March 30, 2025 at 11:34:16 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✗ Maple

ode:=diff(y(x),x) = exp(-1/100*x*y(x)^2); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==Exp[-1/100*x*y[x]^2]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - exp(-x*y(x)**2/100),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - exp(-x*y(x)**2/100) cannot be solved by the lie group method