68.12.49 problem 57

Internal problem ID [17643]
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 : 57
Date solved : Thursday, October 02, 2025 at 02:26:43 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=2 \ln \left (t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=t^2*diff(diff(y(t),t),t)-4*t*diff(y(t),t)-6*y(t) = 2*ln(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = t^{6} c_2 +\frac {c_1}{t}-\frac {\ln \left (t \right )}{3}+\frac {5}{18} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 27

ode=t^2*D[y[t],{t,2}]-4*t*D[y[t],t]-6*y[t]==2*Log[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_2 t^6-\frac {\log (t)}{3}+\frac {c_1}{t}+\frac {5}{18} \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) - 4*t*Derivative(y(t), t) - 6*y(t) - 2*log(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{t} + C_{2} t^{6} - \frac {\log {\left (t \right )}}{3} + \frac {5}{18} \]