56.4.65 problem 62

Internal problem ID [8954]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 62
Date solved : Monday, January 27, 2025 at 05:20:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 17

dsolve(x/(1-x)*diff(y(x),x$2)+x*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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