90.20.8 problem 8

Internal problem ID [25303]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 337
Problem number : 8
Date solved : Thursday, October 02, 2025 at 11:59:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y&=y t \end{align*}

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

ode:=diff(diff(y(t),t),t)-2*y(t) = t*y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \operatorname {AiryAi}\left (t +2\right )+c_2 \operatorname {AiryBi}\left (t +2\right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 20

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

\begin{align*} y(t)&\to c_1 \operatorname {AiryAi}(t+2)+c_2 \operatorname {AiryBi}(t+2) \end{align*}

✓ Sympy. Time used: 0.036 (sec). Leaf size: 15

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

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