74.9.25 problem 36

Internal problem ID [16201]
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 : 36
Date solved : Tuesday, January 28, 2025 at 08:57:03 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 52

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

\[ y = \sqrt {t}\, t^{-\frac {a}{2}} \left (t^{\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_{1} +t^{-\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 57

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

\[ y(t)\to t^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 b+1}-a+1\right )} \left (c_2 t^{\sqrt {a^2-2 a-4 b+1}}+c_1\right ) \]