64.22.3 problem 1 (c)

Internal problem ID [13668]
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 : 1 (c)
Date solved : Tuesday, January 28, 2025 at 05:54:39 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

dsolve(t^2*diff(x(t),t$2)+(2*t^3+7*t)*diff(x(t),t)+(8*t^2+8)*x(t)=0,x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {c_{2} {\mathrm e}^{-t^{2}}+c_{1}}{t^{4}} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 26

DSolve[t^2*D[x[t],{t,2}]+(2*t^3+7*t)*D[x[t],t]+(8*t^2+8)*x[t]==0,{x[t]},t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {2 c_1 e^{-t^2}+c_2}{2 t^4} \]