59.1.4 problem 5.1 (iv)

Internal problem ID [14988]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 5, Trivial differential equations. Exercises page 33
Problem number : 5.1 (iv)
Date solved : Thursday, October 02, 2025 at 09:58:07 AM
CAS classification : [_quadrature]

\begin{align*} z^{\prime }&=x \,{\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(z(x),x) = x*exp(-2*x); 
dsolve(ode,z(x), singsol=all);
 

\[ z = \frac {\left (-2 x -1\right ) {\mathrm e}^{-2 x}}{4}+c_1 \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 22

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

\begin{align*} z(x)&\to -\frac {1}{4} e^{-2 x} (2 x+1)+c_1 \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 20

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

\[ z{\left (x \right )} = C_{1} - \frac {x e^{- 2 x}}{2} - \frac {e^{- 2 x}}{4} \]