63.5.9 problem 2(c)

Internal problem ID [13083]
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)
Date solved : Tuesday, January 28, 2025 at 04:51:45 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.059 (sec). Leaf size: 17

DSolve[D[x[t],t]+2*t*x[t]==Exp[-t^2],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-t^2} (t+c_1) \]