64.22.6 problem 3(b)

Internal problem ID [13592]
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 : Friday, March 14, 2025 at 12:17:26 AM
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*}

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

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

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

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(2*x(t) + sin(t)*Derivative(x(t), (t, 2)) + cos(t)*Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : The given ODE 2*x(t)/cos(t) + tan(t)*Derivative(x(t), (t, 2)) + Derivative(x(t), t) cannot be solved by the factorable group method