65.4.2 problem 9.1 (ii)

Internal problem ID [13732]
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 : Tuesday, January 28, 2025 at 06:00:09 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*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 14

dsolve([diff(x(t),t)+t*x(t)=4*t,x(0) = 2],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 18

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

\[ x(t)\to 4-2 e^{-\frac {t^2}{2}} \]