85.18.9 problem 1 (i)

Internal problem ID [22555]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 52
Problem number : 1 (i)
Date solved : Thursday, October 02, 2025 at 08:50:37 PM
CAS classification : [_separable]

\begin{align*} i^{\prime }&=\frac {t -i t}{t^{2}+1} \end{align*}

With initial conditions

\begin{align*} i \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 15

ode:=diff(i(t),t) = (t-i(t)*t)/(t^2+1); 
ic:=[i(0) = 0]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = 1-\frac {1}{\sqrt {t^{2}+1}} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 18

ode=D[i[t],t]==(t-i[t]*t)/(t^2+1); 
ic={i[0]==0}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to 1-\frac {1}{\sqrt {t^2+1}} \end{align*}

✓ Sympy. Time used: 0.169 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
i = Function("i") 
ode = Eq(Derivative(i(t), t) - (-t*i(t) + t)/(t**2 + 1),0) 
ics = {i(0): 0} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = 1 - \frac {1}{\sqrt {t^{2} + 1}} \]