65.10.3 problem 17.3

Internal problem ID [13786]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 17, Reduction of order. Exercises page 162
Problem number : 17.3
Date solved : Tuesday, January 28, 2025 at 06:03:27 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right )&=0 \end{align*}

Using reduction of order method given that one solution is

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

✗ Solution by Maple

dsolve([(t*cos(t)-sin(t))*diff(x(t),t$2)-diff(x(t),t)*t*sin(t)-x(t)*sin(t)=0,t],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[(t*Cos[t]-Sin[t])*D[x[t],{t,2}]-D[x[t],t]*t*Sin[t]-x[t]*Sin[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

Not solved