64.21.1 problem 1 (a)

Internal problem ID [13591]
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 11.6, Exercises page 567
Problem number : 1 (a)
Date solved : Monday, March 31, 2025 at 08:02:03 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=t*diff(diff(x(t),t),t)-2*diff(x(t),t)+9*t^5*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \sin \left (t^{3}\right )+c_2 \cos \left (t^{3}\right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 20

ode=t*D[x[t],{t,2}]-2*D[x[t],t]+9*t^5*x[t]==0; 
ic={}; 
DSolve[{ode,ic},{x[t]},t,IncludeSingularSolutions->True]
 

\[ x(t)\to c_1 \cos \left (t^3\right )+c_2 \sin \left (t^3\right ) \]

✓ Sympy. Time used: 0.186 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(9*t**5*x(t) + t*Derivative(x(t), (t, 2)) - 2*Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = t^{\frac {3}{2}} \left (C_{1} J_{\frac {1}{2}}\left (t^{3}\right ) + C_{2} Y_{\frac {1}{2}}\left (t^{3}\right )\right ) \]