63.5.9 problem 2(c)

Internal problem ID [13012]
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 : Monday, March 31, 2025 at 07:30:47 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(x(t),t)+2*t*x(t) = exp(-t^2); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \left (t +c_1 \right ) {\mathrm e}^{-t^{2}} \]

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 17

ode=D[x[t],t]+2*t*x[t]==Exp[-t^2]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.216 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(2*t*x(t) + Derivative(x(t), t) - exp(-t**2),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (C_{1} + t\right ) e^{- t^{2}} \]