76.11.1 problem 1

Internal problem ID [17545]
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 : Tuesday, January 28, 2025 at 10:43:11 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 28

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

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