Internal problem ID [11670]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 8, Separable equations. Exercises page 72
Problem number: 8.4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {i^{\prime }-p \left (t \right ) i=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(i(t),t)=p(t)*i(t),i(t), singsol=all)
\[ i \left (t \right ) = c_{1} {\mathrm e}^{\int p \left (t \right )d t} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 25
DSolve[i'[t]==p[t]*i[t],i[t],t,IncludeSingularSolutions -> True]
\begin{align*} i(t)\to c_1 \exp \left (\int _1^tp(K[1])dK[1]\right ) i(t)\to 0 \end{align*}