Internal problem ID [6413]
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]]
\[ \boxed {y^{\prime \prime }-y x -x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(diff(y(x),x$2)-x*y(x)-x=0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {AiryAi}\left (x \right ) c_{2} +\operatorname {AiryBi}\left (x \right ) c_{1} -1 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 28
DSolve[y''[x]-x*y[x]-x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \pi \operatorname {AiryAiPrime}(x) \operatorname {AiryBi}(x)+c_2 \operatorname {AiryBi}(x)+\operatorname {AiryAi}(x) (-\pi \operatorname {AiryBiPrime}(x)+c_1) \\ \end{align*}