4.1.16 problem 16

Internal problem ID [1113]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 04:22:10 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 11

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

\begin{align*} y(t)&\to \frac {\sin (t)}{t^2} \end{align*}

✓ Sympy. Time used: 0.232 (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)
 

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