12.4.2 problem 2

Internal problem ID [1609]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 2
Date solved : Saturday, March 29, 2025 at 11:07:29 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==(Exp[x]+y[x])/(x^2+y[x]^2); 
ic={}; 
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) - (y(x) + exp(x))/(x**2 + y(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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