85.3.3 problem 3 (b)

Internal problem ID [22439]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. C Exercises at page 14
Problem number : 3 (b)
Date solved : Thursday, October 02, 2025 at 08:39:26 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 12

ode:=diff(y(x),x) = exp(y(x)); 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\ln \left (-x +2\right ) \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to -\log (2-x) \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \log {\left (- \frac {1}{x - 2} \right )} \]