7.2.16 problem 20

Internal problem ID [2314]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 05:26:32 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{t}&=\frac {1}{t^{2}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(y(t),t)+1/t*y(t) = 1/t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\ln \left (t \right )+c_1}{t} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 14

ode=D[y[t],t]+1/t*y[t]==1/t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {\log (t)+c_1}{t} \end{align*}

✓ Sympy. Time used: 0.213 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) + y(t)/t - 1/t**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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