76.5.25 problem 26

Internal problem ID [17374]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 26
Date solved : Monday, March 31, 2025 at 04:09:46 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

\begin{align*} y^{\prime }-4 \,{\mathrm e}^{x} y^{2}&=y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {{\mathrm e}^{x}}{-2 \,{\mathrm e}^{2 x}+c_1} \]

✓ Mathematica. Time used: 0.219 (sec). Leaf size: 29

ode=D[y[x],x]-4*Exp[x]*y[x]^2==y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {e^x}{2 e^{2 x}-c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.223 (sec). Leaf size: 14

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

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