59.4.2 problem 9.1 (ii)

Internal problem ID [15013]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 9, First order linear equations and the integrating factor. Exercises page 86
Problem number : 9.1 (ii)
Date solved : Thursday, October 02, 2025 at 10:01:05 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }+x t&=4 t \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 14

ode:=diff(x(t),t)+t*x(t) = 4*t; 
ic:=[x(0) = 2]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = 4-2 \,{\mathrm e}^{-\frac {t^{2}}{2}} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 18

ode=D[x[t],t]+t*x[t]==4*t; 
ic={x[0]==2}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 4-2 e^{-\frac {t^2}{2}} \end{align*}

✓ Sympy. Time used: 0.180 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t*x(t) - 4*t + Derivative(x(t), t),0) 
ics = {x(0): 2} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = 4 - 2 e^{- \frac {t^{2}}{2}} \]