70.11.1 problem 1

Internal problem ID [18832]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.1 (Definitions and examples). Problems at page 214
Problem number : 1
Date solved : Thursday, October 02, 2025 at 03:31:15 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }+y t&=0 \end{align*}

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

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 28

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

\begin{align*} y(t)&\to c_1 \operatorname {AiryAi}\left (\sqrt [3]{-1} t\right )+c_2 \operatorname {AiryBi}\left (\sqrt [3]{-1} t\right ) \end{align*}

✓ Sympy. Time used: 0.032 (sec). Leaf size: 15

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

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