85.3.2 problem 3 (a)

Internal problem ID [22438]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. C Exercises at page 14
Problem number : 3 (a)
Date solved : Thursday, October 02, 2025 at 08:39:25 PM
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,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 8

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

\begin{align*} y(x)&\to e^x \end{align*}

✓ Sympy. Time used: 0.019 (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)
 

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