71.6.1 problem 1

Internal problem ID [14328]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 1
Date solved : Wednesday, March 05, 2025 at 10:45:53 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 10

ode:=diff(y(x),x) = 3*y(x); 
ic:=y(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 12

ode=D[y[x],x]==3*y[x]; 
ic={y[0]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -e^{3 x} \]

✓ Sympy. Time used: 0.102 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = - e^{3 x} \]