Internal problem ID [10389]
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 1.4.1. Integrating factors. Exercises page
41
Problem number: 2(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{\prime }+2 x t -{\mathrm e}^{-t^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(x(t),t)+2*t*x(t)=exp(-t^2),x(t), singsol=all)
\[ x \left (t \right ) = \left (t +c_{1} \right ) {\mathrm e}^{-t^{2}} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 17
DSolve[x'[t]+2*t*x[t]==Exp[-t^2],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t^2} (t+c_1) \\ \end{align*}