89.1.8 problem 8

Internal problem ID [24243]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 21
Problem number : 8
Date solved : Thursday, October 02, 2025 at 10:01:24 PM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{2 x} y-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=y(x)*exp(2*x)-(4+exp(2*x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sqrt {4+{\mathrm e}^{2 x}} \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 24

ode=(y[x]*Exp[2*x])-(4+Exp[2*x])*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \sqrt {e^{2 x}+4}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.168 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(exp(2*x) + 4)*Derivative(y(x), x) + y(x)*exp(2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sqrt {e^{2 x} + 4} \]