17.1.5 problem 1(e)

Internal problem ID [4095]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 1(e)
Date solved : Tuesday, September 30, 2025 at 07:02:37 AM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{2 y}+\left (1+x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=exp(2*y(x))+(1+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\ln \left (2\right )}{2}-\frac {\ln \left (\ln \left (1+x \right )+c_1 \right )}{2} \]

✓ Mathematica. Time used: 0.215 (sec). Leaf size: 21

ode=Exp[2*y[x]]+(1+x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2} \log (2 (\log (x+1)-c_1)) \end{align*}

✓ Sympy. Time used: 0.475 (sec). Leaf size: 44

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

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