32.5.11 problem Exercise 11.12, page 97

Internal problem ID [5849]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.12, page 97
Date solved : Tuesday, March 04, 2025 at 11:48:19 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=\frac {3 \,{\mathrm e}^{-2 x}}{4} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(y(x),x)+2*y(x) = 3/4*exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\left (3 x +4 c_{1} \right ) {\mathrm e}^{-2 x}}{4} \]

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 22

ode=D[y[x],x]+2*y[x]==3/4*Exp[-2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} e^{-2 x} (3 x+4 c_1) \]

✓ Sympy. Time used: 0.151 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) + Derivative(y(x), x) - 3*exp(-2*x)/4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + \frac {3 x}{4}\right ) e^{- 2 x} \]