51.1.6 problem 3. direct method

Internal problem ID [8217]
Book : A course in Ordinary Differential Equations. by Stephen A. Wirkus, Randall J. Swift. CRC Press NY. 2015. 2nd Edition
Section : Chapter 8. Series Methods. section 8.2. The Power Series Method. Problems Page 603
Problem number : 3. direct method
Date solved : Wednesday, March 05, 2025 at 05:32:28 AM
CAS classification : [`y=_G(x,y')`]

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

With initial conditions

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

✗ Maple

ode:=diff(y(x),x) = y(x)+x*exp(y(x)); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

TypeError : argument of type NegativeOne is not iterable