85.27.5 problem 5

Internal problem ID [22597]
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 60
Problem number : 5
Date solved : Thursday, October 02, 2025 at 08:54:50 PM
CAS classification : [[_2nd_order, _quadrature]]

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

With initial conditions

\begin{align*} i \left (0\right )&=2 \\ i^{\prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 18

ode:=diff(diff(i(t),t),t) = t^2+1; 
ic:=[i(0) = 2, D(i)(0) = 3]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = \frac {\left (t^{2}+3\right )^{2}}{12}+3 t +\frac {5}{4} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 22

ode=D[i[t],{t,2}]==t^2+1; 
ic={i[0]==2,Derivative[1][i][0] ==3}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to \frac {1}{12} \left (t^4+6 t^2+36 t+24\right ) \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
i = Function("i") 
ode = Eq(-t**2 + Derivative(i(t), (t, 2)) - 1,0) 
ics = {i(0): 2, Subs(Derivative(i(t), t), t, 0): 3} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = \frac {t^{4}}{12} + \frac {t^{2}}{2} + 3 t + 2 \]