74.9.26 problem 44

Internal problem ID [16202]
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 : 44
Date solved : Tuesday, January 28, 2025 at 08:57:06 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (36 t^{2}-1\right ) y&=0 \end{align*}

Using reduction of order method given that one solution is

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

✓ Solution by Maple

Time used: 0.194 (sec). Leaf size: 21

dsolve([4*t^2*diff(y(t),t$2)+4*t*diff(y(t),t)+(36*t^2-1)*y(t)=0,1/t^(1/2)],singsol=all)
 

\[ y = \frac {c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right )}{\sqrt {t}} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 39

DSolve[4*t^2*D[y[t],{t,2}]+4*t*D[y[t],t]+(36*t^2-1)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{-3 i t} \left (6 c_1-i c_2 e^{6 i t}\right )}{6 \sqrt {t}} \]