Internal problem ID [6414]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x$2)-x*y(x)-x=0,y(x), singsol=all)
\[ y \relax (x ) = \AiryAi \relax (x ) c_{2}+\AiryBi \relax (x ) c_{1}-1 \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 28
DSolve[y''[x]-x*y[x]-x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \pi \text {Ai}'(x) \text {Bi}(x)+c_2 \text {Bi}(x)+\text {Ai}(x) (-\pi \text {Bi}'(x)+c_1) \\ \end{align*}