56.4.65 problem 62

Internal problem ID [8954]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 62
Date solved : Sunday, March 30, 2025 at 01:56:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \frac {x y^{\prime \prime }}{1-x}+x y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 20

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

\[ y(x)\to c_1 \operatorname {AiryAi}(x-1)+c_2 \operatorname {AiryBi}(x-1) \]

✓ Sympy. Time used: 0.078 (sec). Leaf size: 15

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

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