65.4.7 problem 9.1 (vii)

Internal problem ID [13737]
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 (vii)
Date solved : Tuesday, January 28, 2025 at 06:00:19 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }+5 x&=t \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(diff(x(t),t)+5*x(t)=t,x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {t}{5}-\frac {1}{25}+{\mathrm e}^{-5 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 30

DSolve[D[x[t],t]+5*x[t]==t,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-5 t} \left (\int _1^te^{5 K[1]} K[1]dK[1]+c_1\right ) \]