74.9.13 problem 23

Internal problem ID [16189]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 08:56:51 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t -y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(t^2*diff(y(t),t$2)+t*diff(y(t),t)-y(t)=0,y(t), singsol=all)
 

\[ y = \frac {c_{2} t^{2}+c_{1}}{t} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 16

DSolve[t^2*D[y[t],{t,2}]+t*D[y[t],t]-y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {c_1}{t}+c_2 t \]