23.1.130 problem 134

Internal problem ID [4737]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 134
Date solved : Tuesday, September 30, 2025 at 08:20:43 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 22

ode:=diff(y(x),x) = exp(x)*(a+b*exp(-y(x))); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (\frac {a}{{\mathrm e}^{\left ({\mathrm e}^{x}+c_1 \right ) a}-b}\right ) \]

✓ Mathematica. Time used: 0.643 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \log \left (\frac {-b+e^{a \left (e^x+c_1\right )}}{a}\right ) \end{align*}

✓ Sympy. Time used: 0.216 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \log {\left (e^{a \left (C_{1} + e^{x}\right )} - \frac {b}{a} \right )} \]