86.2.8 problem 8

Internal problem ID [23082]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3c at page 50
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:19:36 PM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{y} \left (x y^{\prime }+1\right )&=5 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 22

ode:=exp(y(x))*(1+x*diff(y(x),x)) = 5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (\frac {x}{-1+5 x \,{\mathrm e}^{c_1}}\right )-c_1 \]

✓ Mathematica. Time used: 0.339 (sec). Leaf size: 22

ode=Exp[ y[x] ]*(1+x*D[y[x],x]) ==5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log \left (5+\frac {e^{c_1}}{x}\right )\\ y(x)&\to \log (5) \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x*Derivative(y(x), x) + 1)*exp(y(x)) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \log {\left (\frac {C_{1}}{x} + 5 \right )} \]