74.9.28 problem 46

Internal problem ID [16204]
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 : 46
Date solved : Tuesday, January 28, 2025 at 08:57:07 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=\frac {\sin \left (t \right )}{t^{2}} \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved