65.7.1 problem 1

Internal problem ID [15709]
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 : Thursday, October 02, 2025 at 10:23:44 AM
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: 0.022 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.017 (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]
 

\begin{align*} y(x)&\to \frac {1}{4} \left (5 e^{4 x}-1\right ) \end{align*}

✓ Sympy. Time used: 0.075 (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)
 

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