65.4.14 problem 14

Internal problem ID [15673]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:22:48 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+3 y&=1 \end{align*}

With initial conditions

\begin{align*} y \left (-2\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 14

ode:=diff(y(x),x)+3*y(x) = 1; 
ic:=[y(-2) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {1}{3}+\frac {2 \,{\mathrm e}^{-6-3 x}}{3} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 20

ode=D[y[x],x]+3*y[x]==1; 
ic={y[-2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{3} e^{-3 (x+2)}+\frac {1}{3} \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) + Derivative(y(x), x) - 1,0) 
ics = {y(-2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {1}{3} + \frac {2 e^{- 3 x}}{3 e^{6}} \]