65.3.8 problem 8.4

Internal problem ID [13647]
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
Date solved : Wednesday, March 05, 2025 at 10:06:22 PM
CAS classification : [_separable]

\begin{align*} i^{\prime }&=p \left (t \right ) i \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

ode:=diff(i(t),t) = p(t)*i(t); 
dsolve(ode,i(t), singsol=all);
 

\[ i = c_{1} {\mathrm e}^{\int pd t} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 25

ode=D[i[t],t]==p[t]*i[t]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.289 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
i = Function("i") 
p = Function("p") 
ode = Eq(-i(t)*p(t) + Derivative(i(t), t),0) 
ics = {} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = C_{1} e^{\int p{\left (t \right )}\, dt} \]