68.12.47 problem 55

Internal problem ID [17641]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 55
Date solved : Thursday, October 02, 2025 at 02:26:41 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=\ln \left (t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=t^2*diff(diff(y(t),t),t)+3*t*diff(y(t),t)+y(t) = ln(t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 22

ode=t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+y[t]==Log[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {-2 t+(t+c_2) \log (t)+c_1}{t} \end{align*}

✓ Sympy. Time used: 0.141 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) + 3*t*Derivative(y(t), t) + y(t) - log(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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