Internal problem ID [6533]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 62.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\frac {x y^{\prime \prime }}{1-x}+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.07 (sec). Leaf size: 17
dsolve(x/(1-x)*diff(y(x),x$2)+x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \AiryAi \left (x -1\right )+c_{2} \AiryBi \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[x/(1-x)*y''[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \text {Ai}(x-1)+c_2 \text {Bi}(x-1) \\ \end{align*}