64.21.1 problem 1 (a)

Internal problem ID [13662]
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 : Tuesday, January 28, 2025 at 05:54:31 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*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

\[ x \left (t \right ) = c_{1} \sin \left (t^{3}\right )+c_{2} \cos \left (t^{3}\right ) \]

✓ Solution by Mathematica

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

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

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