76.12.18 problem 30

Internal problem ID [17574]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 10:44:24 AM
CAS classification : [[_Emden, _Fowler]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=t \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

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

\[ y = \frac {c_{2} t^{3}+c_{1}}{t^{2}} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 16

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

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