76.2.16 problem 16

Internal problem ID [17281]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 16
Date solved : Monday, March 31, 2025 at 03:48:37 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {2 y}{t}&=\frac {\cos \left (t \right )}{t^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (\pi \right )&=0 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 10

ode:=diff(y(t),t)+2*y(t)/t = cos(t)/t^2; 
ic:=y(Pi) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {\sin \left (t \right )}{t^{2}} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 19

ode=D[y[t],t]+2/t*y[t]==Cos[t]/t^2; 
ic={y[Pi]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {\int _{\pi }^t\cos (K[1])dK[1]}{t^2} \]

✓ Sympy. Time used: 0.345 (sec). Leaf size: 8

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

\[ y{\left (t \right )} = \frac {\sin {\left (t \right )}}{t^{2}} \]