64.22.12 problem 7(a)

Internal problem ID [13677]
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 : 7(a)
Date solved : Tuesday, January 28, 2025 at 05:54:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }+\left (1+t \right ) x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 21

dsolve(diff(x(t),t$2)+(t+1)*x(t)=0,x(t), singsol=all)
 

\[ x \left (t \right ) = c_{1} \operatorname {AiryAi}\left (-t -1\right )+c_{2} \operatorname {AiryBi}\left (-t -1\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 32

DSolve[D[x[t],{t,2}]+(t+1)*x[t]==0,{x[t]},t,IncludeSingularSolutions -> True]
 

\[ x(t)\to c_1 \operatorname {AiryAi}\left (\sqrt [3]{-1} (t+1)\right )+c_2 \operatorname {AiryBi}\left (\sqrt [3]{-1} (t+1)\right ) \]