88.11.1 problem 1

Internal problem ID [24048]
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 : Sunday, October 12, 2025 at 05:55:23 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 27

ode:=[diff(y(x),x) = -2, diff(z(x),x) = x*exp(y(x)+2*x)]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 28

ode={D[y[x],x]==-2,D[z[x],x]==x*Exp[y[x]+2*x]}; 
ic={}; 
DSolve[{ode,ic},{y[x],z[x]},x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.058 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq(Derivative(y(x), x) + 2,0),Eq(-x*exp(2*x + y(x)) + Derivative(z(x), x),0)] 
ics = {} 
dsolve(ode,func=[y(x),z(x)],ics=ics)
 

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