63.5.13 problem 3(a)

Internal problem ID [13087]
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 : 3(a)
Date solved : Tuesday, January 28, 2025 at 04:51:52 AM
CAS classification : [_linear]

\begin{align*} x^{\prime }+\frac {5 x}{t}&=1+t \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=1 \end{align*}

✓ Solution by Maple

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

dsolve([diff(x(t),t)+(5/t)*x(t)=1+t,x(1) = 1],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {t^{2}}{7}+\frac {t}{6}+\frac {29}{42 t^{5}} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 27

DSolve[{D[x[t],t]+(5/t)*x[t]==1+t,{x[1]==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {\int _1^t\left (K[1]^6+K[1]^5\right )dK[1]+1}{t^5} \]