Internal problem ID [11651]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {z^{\prime }=x \,{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(z(x),x)=x*exp(-2*x),z(x), singsol=all)
\[ z \left (x \right ) = -\frac {\left (2 x +1\right ) {\mathrm e}^{-2 x}}{4}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 22
DSolve[z'[x]==x*Exp[-2*x],z[x],x,IncludeSingularSolutions -> True]
\[ z(x)\to -\frac {1}{4} e^{-2 x} (2 x+1)+c_1 \]