68.14.31 problem 31

Internal problem ID [17723]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 31
Date solved : Thursday, October 02, 2025 at 02:27:22 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime }&=1 \end{align*}

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

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

\[ y = \frac {c_2 \,t^{2}}{2}-\ln \left (t \right ) c_1 t +t +c_3 \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 25

ode=t^2*Log[t]*D[ y[t],{t,3}]-t*D[y[t],{t,2}]+D[y[t],t]==1; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {c_1 t^2}{2}+t-c_2 t \log (t)+c_3 \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*log(t)*Derivative(y(t), (t, 3)) - t*Derivative(y(t), (t, 2)) + Derivative(y(t), t) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : CRootOf is not supported over ZZ[log(t)]