84.2.3 problem 1.8

Internal problem ID [22072]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 1. Basic concepts. Supplementary problems
Problem number : 1.8
Date solved : Thursday, October 02, 2025 at 08:23:25 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} t^{2} s^{\prime \prime }-t s^{\prime }&=1-\sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 34

ode:=t^2*diff(diff(s(t),t),t)-t*diff(s(t),t) = 1-sin(t); 
dsolve(ode,s(t), singsol=all);
 

\[ s = \frac {\left (t^{2}+2\right ) \operatorname {Si}\left (t \right )}{4}+\frac {t^{2} c_1}{2}+\frac {\cos \left (t \right ) t}{4}+c_2 -\frac {\ln \left (t \right )}{2}+\frac {\sin \left (t \right )}{4} \]

✓ Mathematica. Time used: 60.098 (sec). Leaf size: 50

ode=t^2*D[s[t],{t,2}]-t*D[s[t],t]==1-Sin[t]; 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to \int _1^t\frac {2 c_1 K[1]^2+\text {Si}(K[1]) K[1]^2+\cos (K[1]) K[1]+\sin (K[1])-1}{2 K[1]}dK[1]+c_2 \end{align*}

✓ Sympy. Time used: 0.885 (sec). Leaf size: 39

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

\[ s{\left (t \right )} = C_{1} + C_{2} t^{2} + \frac {t^{2} \operatorname {Si}{\left (t \right )}}{4} + \frac {t \cos {\left (t \right )}}{4} - \frac {\log {\left (t \right )}}{2} + \frac {\sin {\left (t \right )}}{4} + \frac {\operatorname {Si}{\left (t \right )}}{2} \]