74.14.31 problem 31

Internal problem ID [16436]
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 : Tuesday, January 28, 2025 at 09:07:56 AM
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*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(t^2*ln(t)*diff(y(t),t$3)-t*diff(y(t),t$2)+diff(y(t),t)=1,y(t), singsol=all)
 

\[ y = \frac {c_{2} t^{2}}{2}-\ln \left (t \right ) c_{1} t +t +c_{3} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 25

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

\[ y(t)\to \frac {c_1 t^2}{2}+t-c_2 t \log (t)+c_3 \]