88.11.2 problem 1

Internal problem ID [24049]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 54
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:55:13 PM
CAS classification : system_of_ODEs

\begin{align*} y^{\prime }+y&={\mathrm e}^{x}\\ z^{\prime }\left (x \right )&=y \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 31

ode:=[diff(y(x),x)+y(x) = exp(x), diff(z(x),x) = y(x)]; 
dsolve(ode);
 

\begin{align*} y \left (x \right ) &= \frac {{\mathrm e}^{x}}{2}+{\mathrm e}^{-x} c_2 \\ z \left (x \right ) &= \frac {{\mathrm e}^{x}}{2}-{\mathrm e}^{-x} c_2 +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 48

ode={D[y[x],x]+y[x]==Exp[x],D[z[x],x]==y[x]}; 
ic={}; 
DSolve[{ode,ic},{y[x],z[x]},x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^x}{2}+c_1 e^{-x}\\ z(x)&\to \frac {e^x}{2}+c_1 \left (-e^{-x}\right )-\frac {1}{2}+c_1+c_2 \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 26

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

\[ \left [ y{\left (x \right )} = - C_{1} e^{- x} + \frac {e^{x}}{2}, \ z{\left (x \right )} = C_{1} e^{- x} + C_{2} + \frac {e^{x}}{2}\right ] \]