86.8.9 problem 9

Internal problem ID [23169]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5e at page 91
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:23:44 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} s^{\prime \prime }&=5 t^{2}-7 t \end{align*}

With initial conditions

\begin{align*} s \left (0\right )&=0 \\ s \left (1\right )&={\frac {1}{4}} \\ \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 16

ode:=diff(diff(s(t),t),t) = 5*t^2-7*t; 
ic:=[s(0) = 0, s(1) = 1/4]; 
dsolve([ode,op(ic)],s(t), singsol=all);
 

\[ s = \frac {5}{12} t^{4}-\frac {7}{6} t^{3}+t \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 21

ode=D[s[t],{t,2}]==5*t^2-7*t; 
ic={s[0]==0,s[1]==1/4}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to \frac {5 t^4}{12}-\frac {7 t^3}{6}+t \end{align*}

✓ Sympy. Time used: 0.050 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(-5*t**2 + 7*t + Derivative(s(t), (t, 2)),0) 
ics = {s(0): 0, s(1): 1/4} 
dsolve(ode,func=s(t),ics=ics)
 

\[ s{\left (t \right )} = \frac {5 t^{4}}{12} - \frac {7 t^{3}}{6} + t \]