Internal problem ID [10345]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 1, First order differential equations. Section 1.2 Antiderivatives. Exercises page
19
Problem number: 4(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-t \,{\mathrm e}^{-2 t}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(x(t),t)=t*exp(-2*t),x(t), singsol=all)
\[ x \left (t \right ) = -\frac {\left (2 t +1\right ) {\mathrm e}^{-2 t}}{4}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 22
DSolve[x'[t]==t*Exp[-2*t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {1}{4} e^{-2 t} (2 t+1)+c_1 \\ \end{align*}