74.9.20 problem 31

Internal problem ID [16196]
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 : 31
Date solved : Tuesday, January 28, 2025 at 08:56:58 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} y^{\prime \prime }+4 y^{\prime } t -4 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=\frac {1}{t^{4}} \end{align*}

✓ Solution by Maple

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

dsolve([t^2*diff(y(t),t$2)+4*t*diff(y(t),t)-4*y(t)=0,1/t^4],singsol=all)
 

\[ y = \frac {c_{2} t^{5}+c_{1}}{t^{4}} \]

✓ Solution by Mathematica

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

DSolve[t^2*D[y[t],{t,2}]+4*t*D[y[t],t]-4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {c_1}{t^4}+c_2 t \]