10.1.16 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 : Saturday, March 29, 2025 at 10:39:26 PM
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,ic],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.031 (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]
 

\[ y(t)\to \frac {\sin (t)}{t^2} \]

✓ Sympy. Time used: 0.373 (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)
 

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