68.3.28 problem 23

Internal problem ID [17175]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 23
Date solved : Thursday, October 02, 2025 at 01:49:15 PM
CAS classification : [_linear]

\begin{align*} t y^{\prime }+y&=t \sin \left (t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (\pi \right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 16

ode:=t*diff(y(t),t)+y(t) = t*sin(t); 
ic:=[y(Pi) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {\sin \left (t \right )-t \cos \left (t \right )}{t} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 24

ode=t*D[y[t],t]+y[t]==t*Sin[t]; 
ic={y[Pi]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {\int _{\pi }^tK[1] \sin (K[1])dK[1]+\pi }{t} \end{align*}

✓ Sympy. Time used: 0.178 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = - \cos {\left (t \right )} + \frac {\sin {\left (t \right )}}{t} \]