64.22.6 problem 3(b)

Internal problem ID [13671]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 11, The nth order homogeneous linear differential equation. Section 11.8, Exercises page 583
Problem number : 3(b)
Date solved : Tuesday, January 28, 2025 at 08:24:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x&=0 \end{align*}

✓ Solution by Maple

Time used: 6.404 (sec). Leaf size: 39

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

\[ x \left (t \right ) = c_{1} \operatorname {HeunG}\left (2, 2, 0, 1, \frac {1}{2}, 1, \sin \left (t \right )+1\right )+c_{2} \sin \left (\frac {\pi }{4}+\frac {t}{2}\right ) \operatorname {HeunG}\left (2, \frac {13}{4}, \frac {1}{2}, \frac {3}{2}, \frac {3}{2}, 1, \sin \left (t \right )+1\right ) \]

✗ Solution by Mathematica

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

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

Not solved