68.5.30 problem 30

Internal problem ID [17281]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 30
Date solved : Thursday, October 02, 2025 at 02:00:47 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=\frac {4}{\pi } \\ \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 12

ode:=t*diff(y(t),t)+y(t) = cos(t); 
ic:=[y(1/2*Pi) = 4/Pi]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {\sin \left (t \right )+1}{t} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 25

ode=t*D[y[t],t]+y[t]==Cos[t]; 
ic={y[Pi/2]==4/Pi}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {\int _{\frac {\pi }{2}}^t\cos (K[1])dK[1]+2}{t} \end{align*}

✓ Sympy. Time used: 0.158 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), t) + y(t) - cos(t),0) 
ics = {y(pi/2): 4/pi} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {\sin {\left (t \right )} + 1}{t} \]