63.5.14 problem 3(b)

Internal problem ID [13088]
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(b)
Date solved : Tuesday, January 28, 2025 at 04:51:54 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\left (a +\frac {b}{t}\right ) x \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 14

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

\[ x \left (t \right ) = t^{b} {\mathrm e}^{a \left (t -1\right )} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 16

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

\[ x(t)\to e^{a (t-1)} t^b \]