Internal problem ID [11422]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-\left (a +\frac {b}{t}\right ) x=0} \] With initial conditions \begin {align*} [x \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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: 0.053 (sec). Leaf size: 16
DSolve[{x'[t]==(a+b/t)*x[t],{x[1]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{a (t-1)} t^b \]