44.3.22 problem 4(b)

Internal problem ID [9132]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 4(b)
Date solved : Tuesday, September 30, 2025 at 06:05:44 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 14

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

\[ x -\left ({\mathrm e}^{y}+c_1 \right ) y = 0 \]

✓ Mathematica. Time used: 0.14 (sec). Leaf size: 18

ode=y[x]-x*D[y[x],x]==D[y[x],x]*y[x]^2*Exp[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x=e^{y(x)} y(x)+c_1 y(x),y(x)\right ] \]

✓ Sympy. Time used: 0.487 (sec). Leaf size: 12

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

\[ C_{1} + \frac {x}{y{\left (x \right )}} - e^{y{\left (x \right )}} = 0 \]