65.1.4 problem 5.1 (iv)

Internal problem ID [13707]
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 : Tuesday, January 28, 2025 at 05:55:43 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 24

DSolve[D[z[x],x]==x*Exp[-2*x],z[x],x,IncludeSingularSolutions -> True]
 

\[ z(x)\to \int _1^xe^{-2 K[1]} K[1]dK[1]+c_1 \]