74.5.37 problem 38 (c)

Internal problem ID [15930]
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 : 38 (c)
Date solved : Monday, March 31, 2025 at 02:13:41 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = \left (c_2 +c_1 \ln \left (t \right )+\frac {\ln \left (t \right )^{2}}{2}\right ) t \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 25

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

\[ y(t)\to \frac {1}{2} t \left (\log ^2(t)+2 c_2 \log (t)+2 c_1\right ) \]

✓ Sympy. Time used: 0.235 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = \frac {t \left (C_{1} + C_{2} \log {\left (t \right )} + \log {\left (t \right )}^{2}\right )}{2} \]