68.9.28 problem 46

Internal problem ID [17491]
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 : Thursday, October 02, 2025 at 02:24:41 PM
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*}

✗ Maple

ode:=diff(diff(y(t),t),t)+b(t)*diff(y(t),t)+c(t)*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
b = Function("b") 
c = Function("c") 
ode = Eq(b(t)*Derivative(y(t), t) + c(t)*y(t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

TypeError : cannot determine truth value of Relational: t > t