71.7.1 problem 1

Internal problem ID [14343]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 1
Date solved : Wednesday, March 05, 2025 at 10:47:40 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=4 y+1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 12

ode:=diff(y(x),x) = 4*y(x)+1; 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {1}{4}+\frac {5 \,{\mathrm e}^{4 x}}{4} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 18

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

\[ y(x)\to \frac {1}{4} \left (5 e^{4 x}-1\right ) \]

✓ Sympy. Time used: 0.140 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + Derivative(y(x), x) - 1,0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {5 e^{4 x}}{4} - \frac {1}{4} \]