58.22.12 problem 7(a)

Internal problem ID [14958]
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 : Thursday, October 02, 2025 at 09:57:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

ode:=diff(diff(x(t),t),t)+(t+1)*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 32

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

\begin{align*} 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 ) \end{align*}

✓ Sympy. Time used: 0.037 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq((t + 1)*x(t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} Ai\left (- t - 1\right ) + C_{2} Bi\left (- t - 1\right ) \]