44.5.68 problem 58 (a 1)

Internal problem ID [7130]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 58 (a 1)
Date solved : Wednesday, March 05, 2025 at 04:17:38 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 6

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 8

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

\[ y(x)\to e^x \]

✓ Sympy. Time used: 0.060 (sec). Leaf size: 5

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

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